Keep in mind that words do not have uniform definitions for all times and places and contexts. Words can have different meanings in particular contexts and can be defined in a contract or statute to have a meaning different from the common meaning.
"Person" Usually Includes Entities Of Any Kind
This said, usually the term "person" in the law refers to any human being and any trust, estate or entity that is capable of suing and being sued and entering into contracts.
An "entity" in this sense would often include partnerships, limited liability companies, corporations, non-profit associations (whether or not incorporated), business trusts, joint ventures, local governments, states, the federal government and foreign governments.
(I break out trusts and estates separately because there is divided authority in different jurisdictions over whether trusts and estates are entities, or are simply a special hat that the trustee or executor wears that are not entities, which can be relevant in some highly technical situations.)
The term "person" is also often used in the sense that it refers to the principal and not the agent, when an agent is taking action on behalf of the principal.
Thus, if there is a law that says "a person who enters into a real estate contract must disclose that person's taxpayer identification number", and someone with a power of attorney from you signs a real estate contract on your behalf, the power of attorney agent should disclosure your taxpayer identification number and not theirs.
Why Is The Term "Person" Defined So Broadly?
One important reason for using the term "person" to apply to entities as well as human beings, is that it allows for statutes and contract terms or case law legal rules to be stated in very general terms without being wordy in a way that accurately reflects how those legal rules or contract terms should apply to entities.
For example, a statute using the word "person" might say:
A person who is engaged in business in this state must register with
the department of business licenses.
By using the word "person" in this way, the statute wouldn't have to say instead (probably less accurately and less comprehensibly):
Any individual, partnership, limited liability company, corporation,
business trust, non-business trust, estate, governmental entity, or
other entity, including the principal of any agent acting on behalf of
the principal, engaged in business in this state, must register with
the department of business licenses.
The phrasing without the word "person" would be more likely to create loopholes because some kind of entity is omitted, and would be prone to ambiguity because one would have to decide which words that define the kind of persons and entities that are covered modify which other words in the sentence.
Thus, using the word "person" is often makes entities more rather than less accountable to the law, by making legal language more clear and more general (and hence containing fewer loopholes).
"Individual" or "Natural Person"
Usually the term "individual" or "natural person" would mean a human being, although, of course, there are other senses of the word "individual" such as "an individual Widget" referring to exactly one Widget in particular, as opposed to Widgets in general.
Alternative Definitions Of "Person"
There are isolated times when the word "person" would not include minors and incapacitated people who are incapable of suing or entering into contracts in their own name due to lack of legal capacity.
It isn't uncommon to have a definition of "person" in a statute or contract that omits governmental entities, that omits all kinds of entities, or that omits particular kinds of entities (e.g. foreign entities or corporations).
For example, a tax statute might define "person" in a way that includes natural persons and entities, but excludes governments.
Some of the definitions of terms like these in the bankruptcy code are particularly non-intuitive.