To be versed in something is to know it well and have experience with it. If you’re well versed in Middle English literature, you know that Chaucer wrote The Canterbury Tales in 1475. Go you.
Versed comes from the Latin word versari which means basically “to busy oneself, to be engaged.” If you’re versed (sounds like “verst”) in a subject, you’ve busied yourself with it and now you know it well. A history professor is versed in history. Someone with a massive comic book collection is probably versed in superheroes. Sometimes people say a person is well versed instead of versed, but either way, that person knows what they’re talking about.