Definition of jurisprudence.
Jurisprudence has a number of different meanings. In general, though jurisprudence is the philosophy of law.
There are different aspects to jurisprudence and the study of jurisprudence. The most common aspect is the analysis of some given area of law. In that type of jurisprudence, scholars look at an area of law and analyze court cases in that area. They seek to understand the fundamental rules of that area of law by analyzing these cases. For example, I once took a class on slave law in the United States. We read court cases from the time when slavery was legal as a way of understanding what the basic rules of that society were and what it meant (legally) to be a slave or someone who interacted with slaves.
Another important aspect of jurisprudence is more normative. It asks how things should be. This is the area in which scholars ask if judges can and should (for example) stick exactly to the text of the law. They try to determine whether it is better to approach the law in a formalistic way or whether it is better to decide cases more on the basis of what seems equitable.
Jurisprudence, then, can be about what is or it can be about what should be. In both cases, though, it is the study of what the philosophy of the law is.