Etymology: Latin jurisprudentia — jus (law/right) + prudentia (knowledge, skill, foresight): literally "the knowledge or skill of law." The Roman jurist Ulpian (as preserved in Justinian's Digest) called it "the knowledge of things divine and human, the science of the just and the unjust" — the earliest, and still the grandest, job description. The classic definitions (quote briefly, attribute exactly — this is a favourite short question): John Austin: jurisprudence is "the philosophy of positive law" — the general theory of what law actually is, not what it ought to be. Salmond: the "science of the first principles of civil law" — jurisprudence studies the fundamental concepts (right, duty, person, liability) that the civil law presupposes.
Thomas Erskine Holland: "the formal science of positive law" — formal because it studies the form and relations of legal conceptions, not their material content; positive because it concerns law as it exists, not as it should be. Roscoe Pound (the functional view): jurisprudence is the science of law in the wide sense — including how law works as an instrument of social engineering (Unit 2.4).
Julius Stone / R.W.M. Dias (the modern view): the lawyer's extraversion — law examined in its relations with logic, ethics, history, sociology, psychology and power. Working synthesis (write this in exams): Jurisprudence is the philosophy and general theory of law — the discipline that asks what law is, where it comes from, what it is for, and how its fundamental concepts fit together, using the methods of philosophy, history and the social sciences. The one-line picture for a law student: doctrinal legal science tells you what the law of Nepal says; jurisprudence asks what it means for anything to be "law" at all — the grammar beneath the language.