Legal Theory and Philosophy of Law
There are two different meanings of the word Jurisprudence
A heavy word for the study or knowledge of the law. If a judge or law lecturer were to refer to "the role of freedom of contract in our jurisprudence" for example, this is the sense intended (this is the sense @ohwilleke refers to in his answer).
The second meaning - and the more usual meaning nowadays, particularly in in academic circles (I note you are studying law so this is probably the meaning you are asking about) - could be described as the philosophy of law.
In Legal Philosophies (1997) J W Harris says (p.1)
Jurisprudence is a ragbag. Into it are cast all kinds of general
speculations about the law. What is it for? What does it achieve?
Should we value it? How is it to be improved? Is it dispensable? Who
makes it? Where do we find it? What is its relation to morality, to
justice, to politics, to social practices, or to naked force? Should
we obey it? Whom does it serve? These are the questions of which
general jurisprudence is comprised. They can be ignored, but they will
no go away...
Jurisprudence has to entrench on [the disciplines of moral and
political philosophers] at many points, as well as upon those of
social and political theory. It is a scavenger, as well as a ragbag;
having no perimeter to its field of enquiry, save that what is studied
must have a bearing on some general speculation about law.
If jurisprudence has a heartland all its own, it is legal theory
Much discussion about moral claims of the law (and moral claims on the
law) takes the concept of law itself for granted. Yet, answers to such
questions may turn on what picture of law we have. Legal theory asks:
What is the nature of law (everywhere, or just in the modern state)?
In a three year English undergraduate law degree, Jurisprudence has traditionally been studied as a compulsory module in the third year which concentrates on legal theory. One thing students immediately notice is that the exact scope and definition of jurisprudence is disputed (which can be discomforting since all the other modules they have hitherto studied - Contract, Tort, Crime, etc- have clear definitions). This uncertainty is exacerbated by the fact that legal theories which come under the umbrella term of legal positivism have as one of their central themes the proposition that jurisprudence should only be concerned with positive law and that legal theory need not (and should not) look outside to ideas of morality or natural law.
In other words not only do different legal theories have different explanations of the phenomenon of law, but they actually disagree about the scope of what it is they are supposed to be explaining!
Traditionally jurists thought of God as the ultimate law-giver whose laws were written on human hearts (conscience). This is the "natural law" which human legislators add to by creating "positive law". For example murder is contrary to natural law but you need human laws to define the different categories of homicide, the prescribed penalties, and the procedure by which accusations are tried and decided. You also need human laws to define the circumstances in which a contract comes into being etc.
Note: positive in used in its old original meaning of "laid down" as distinct from natural. It is nothing to do with the modern meaning of positive as being the opposite of negative.
William Blackstone, in Vol. 1, Commentaries on the Laws of England (1765) Page 27, wrote:
This will of his maker is called the law of nature. For as God, when
he created matter, and endued it with a principle of mobility,
established certain rules for the perpetual direction of that motion;
so, when he created man, and endued him with freewill to conduct
himself in all parts of life, he laid down certain immutable laws of
human nature, whereby that freewill is in some degree regulated and
restrained, and gave him also the faculty of reason to discover the
purport of those laws. Considering the creator only as a being of
infinite power, he was able unquestionably to have prescribed whatever
laws he pleased to his creature, man, however unjust or severe. But as
be is also a being of infinite wisdom, he has laid down only such laws
as were founded in those relations of justice, that existed in the
nature of things antecedent to any positive precept. These are the
eternal, immutable laws of good and evil, to which the creator himself
in all his dispensations conforms; and which he has enabled human
reason to discover, so far as they are necessary for the conduct of
human actions. Such among others are these principles: that we should
live honestly, should hurt nobody, and should render to every one his
due; to which three general precepts Justinian1 has reduced the whole
doctrine of law. This will of his maker is called the law of nature.
For as God, when he created matter, and endued it with a principle of
mobility, established certain rules for the perpetual direction of
that motion; so, when he created man, and endued him with freewill to
conduct himself in all parts of life, he laid down certain immutable
laws of human nature, whereby that freewill is in some degree
regulated and restrained, and gave him also the faculty of reason to
discover the purport of those laws. Considering the creator only as a
being of infinite power, he was able unquestionably to have prescribed
whatever laws he pleased to his creature, man, however unjust or
severe. But as be is also a being of infinite wisdom, he has laid down
only such laws as were founded in those relations of justice, that
existed in the nature of things antecedent to any positive precept.
These are the eternal, immutable laws of good and evil, to which the
creator himself in all his dispensations conforms; and which he has
enabled human reason to discover, so far as they are necessary for the
conduct of human actions. Such among others are these principles: that
we should live honestly, should hurt nobody, and should render to
every one his due; to which three general precepts Justinian has
reduced the whole doctrine of law....
Upon these two foundations, the law of nature and the law of
revelation, depend all human laws; that is to say, no human laws
should be suffered to contradict these. There are, it is true a great
number of indifferent points, in which both the divine law and the
natural leave a man at his own liberty; but which are found necessary
for the benefit of society to be restrained within certain limits. And
herein it is that human laws have their greatest force and efficacy;
for, with regard to such points as are not indifferent, human laws are
only declaratory of, and act in subordination to, the former. To
instance in the case of murder; this is expressly forbidden by the
divine, and demonstrably by the natural law; and from these
prohibitions arises the true unlawfulness of this crime. Those human
laws that annex a punishment to it, do not at all increase its moral
guilt, or superadd any fresh obligation in foro conscientiae [in the
court of conscience] to abstain from its perpetration. Nay, if any
human law should allow or enjoin us to commit it, we are bound to
transgress that human law, or else we must offend both the natural and
the divine. But with regard to matters that are in themselves
indifferent, and are not commanded or forbidden by those superior
laws; such, for instance, as exporting of wool into foreign countries;
here the inferior legislature has scope and opportunity to interpose,
and to make that action unlawful which before was not so...
In the Province of Jurisprudece Determined (1832) John Austin wrote at length about both natural law and positive law and sought to draw a line of distinction between them:
AS one of the Law-Professors at the University of London, I planned
and partly delivered a systematical Course of Lectures on General or
Abstract Jurisprudence. In the ten lectures delivered at the beginning
of my Course, I distinguished positive law (the appropriate matter of
jurisprudence) from various objects with which it is connected by
resemblance, and from various other objects to which it is allied by
analogy. Out of those ten discourses, I have made the treatise which I
now submit to the public, and which I venture to entitle “the
province of jurisprudence determined.”
Determining the characters of positive laws, I determine implicitly
the notion of sovereignty, with the implied or correlative notion of
independent political society. For the essential difference of a
positive law (or the difference that severs it from a law which is not
a positive law) may be stated generally in the following manner.
Every positive law, or every law simply and strictly so called, is set
by a sovereign person, or a sovereign body of persons to a member or
members of the independent political society wherein that person or body > is sovereign or supreme.
Or (changing the phrase) it is set by a monarch, or sovereign number,
to a person or persons in a state of subjection to its author. To
elucidate the nature of sovereignty, and of the independent political
society that sovereignty implies, I examine various topics which I
arrange under the following heads: First, the possible forms or shapes
of supreme political government; second, the limits, real or
imaginary, of supreme political power; thirdly, the origin or causes
of political government and society. Examining those various topics,
I complete my description of the limit or boundary by which positive
law is severed from positive morality. For I distinguish them at
certain points whereat they seemingly blend, or whereat the line which
divides them is not easily perceptitible.
Austin's account of positive law (essentially a command of a sovereign accompanied by a threat of sanction for non-compliance) has been criticised as being simplistic and of failing to provide an adequate explanation of law and legal systems, but to be fair to Austin he never claimed that his theory of positive law could alone explain what happens in legal systems. He recognised the influence of natural law/morality as part of an explanation. He simply wished to define the limits of Jurispudence as an academic subject, which he did narrowly.
Some jurists, however, have subsequently sought to produce theories of law which seek to explain what the phenomenon of law is, and how it works, based only on positive law. Such theorists are called "positivists" and their school of thought is called legal positivism.
In 1960 Hans Kelsen published Reine Rechtslehre which was translated into English in 1967 as The Pure Theory of Law. As the word pure in the title suggests Kelsen's theory is in the legal positivism school of thought - i.e. it seeks to explain law and legal systems by reference only to positive law.
Kelsen himself was a moral relativist but not all legal positivists are necessarily atheists or moral relativists. Some may personally think that natural law/morality is important but nevertheless think that the discipline of law should be "self contained" and should be capable of being completely and satisfactorily explained without brining natural law/morality etc. into it.
Natural lawyers critique the theories of legal positivism by saying that they are incomplete as they leave so much unexplained. Legal Positivists reply that their theories have a restricted scope precisely because everything outside the scope of the theory is not really law at all and so does not need to be explained by the theory.
So you can see that the definition of Jurisprudence is rather woolly but philosophy of law with particular emphasis on competing theories of what the phenomenon of law actually is might be a short rough definition to convey the general idea of Jurisprudence as the word in generally used today.
