There are many ways to answer this question, but for now we shall restrict ourselves to two.

First, there is what we may call a pragmatic reason: the study of Latin can help you in all sorts of practical ways. It has long since been an accepted fact that, thanks to the nearly 60% of English vocabulary deriving from Latin roots, studying Latin boosts one's own English vocabulary, a benefit that manifests itself not least in measurably higher scores on standardized tests. To study Latin requires a much more analytical understanding of how our own language, English, works, so students in Latin almost invariably wind up with a better command of English diction, style, and usage than they had before. Finally, the habits of mind inculcated by studying Latin--close attention to detail and rigorous, logical thinking, for instance--stand one in good stead whatever one's chosen field of study later in life. Time was when an education in Classics was the training required for success in law school, and to this day anyone who has studied Latin, Greek or the Classics in depth will prove attractive to graduate schools or prospective employers--for such a person has proven herself eminently docile--that is, teachable, whatever the skills to be taught may be.

Yet the pragmatic benefits of Latin ought to be considered as happy side-benefits, not as ends in themselves. For studying Latin (or Greek, or both) confers upon the student the same benefit that studying any non-native language does--it opens doors onto a world not one's own, broadens horizons, breaks down the parochial and provincial world-view which most people consider inimical to an educated, cultured, cosmopolitan way of life. To learn Latin via the Oxford Latin Course is to follow the life of one of the greatest lyric poets in any language--Horace--and to learn, though that biography, about one of the watershed events in world history, namely the dissolution of the Roman Republic and the birth of the Principate from its ashes. Building on that foundation, a student of Latin can undertake reading seminal works in the European tradition--not just Horace's Odes, but also Cicero's oratory, Livy's history, Ovid's love poems, Catullus' invective, and Vergil's epic. Reading these works broadens a person's horizons, forcing one to think hard about what it means to be a person.

In short, studying Latin (and the Classics in general) enables one to experience the only kind of life Socrates deemed worth living for a person--the examined, thoughtful, life.