The Wikipedia page of jurisdiction does not help me much to comprehend the concept. In my understanding it basically "law in specific region". I understand the concept is much more than that, but I don't know exactly what. Can you give some examples or analogies? And is there anything that is shared between all jurisdictions?
"Law" refers to rules; "jurisdiction" refers to the situations in which those laws apply.
For example, the United States Constitution is the supreme law of the United States of America. But for the most part, it only applies within the territorial jursidction of the government that enacted it, i.e., places inside the borders of the United States, or to those over whom the United States has personal jurisdiction, i.e., United States citizens, permanent residents, those currently inside its borders.
So the United States Congress could pass a law outlawing the sale of dogs, but it would have no effect on dogs in Canada, as Congress has no jurisdiction over dogs in Canada. Similarly, if a Canadian terrorist (the most dangerous kind, really) launched a missle over the border into the United States, the FBI could not arrest him in Toronto, as they lack jurisdiction to enforce the law outside the United States.
"Jurisdiction" is also a concept that limits the powers of courts to hear cases. "Subject matter jurisdiction" refers to limits on the types of cases the court may hear, and "personal jurisdiction" refers to limits on whose cases the court may hear.
For instance, if the New York Legislature established a small-claims courts to resolve claims for less than $10,000, your case might be dismissed for lack of subject-matter jurisdiction if you sued someone for $10,001, or it might be dismissed for lack of personal jurisdiction if you sued someone who had no connection to New York.
These explanations are admittedly incomplete and imprecise to provide a basic understanding of the concepts, rather than an overwhelming -- and boring -- exposition of the precise meanings of these terms.
LAW is the codified system of rules and processes that permit, regulate, or punish certain activities. It also defines the Jurisdiction where (and by default, where not) these rules etc apply.
JURISDICTION is the extent and limitation (e.g. geographic or procedural) to where certain laws apply. The more common example of 'shared' jurisdiction is international law where different countries agree to incorporate the same, or similar, laws in to their own national statutes.