If a person, a book, or a talk is erudite, it shows a lot of knowledge that comes from careful, long study — not from being quick or street-smart. You have read widely, often in history, literature, languages, or ideas, and it shows. It is a fairly formal, even slightly cool word: a compliment about book-learning. Teachers, critics, and people who like to sound precise use it; you would not usually call a clever child or a good mechanic erudite. Though actually, people also use it with a small smile, as if the person is a bit too bookish, or they use it loosely just to mean “sounds smart.” The heart of the word is still learned, not merely bright. It is mostly an adjective (an erudite historian); as a noun, an erudite (a very learned person) exists but is rare.