Good question!
A pun is a type of joke. The joke is based on the many meanings of one word, usually. Let me give you an example:
"A horse is a very stable animal!"
Even though this joke isn't very funny (it's not going to make you laugh very hard =P), it is still a pun. Here's why: the word "stable" has two uses. Stable, the noun, is a place to keep horses (like a house for them). Stable, the adjective, means that someone is reliable, or that they don't change. In this joke, the person saying it is using "stable" in both ways at the same time.
Puns are usually seen as very "corny" or "cheesy" jokes in English. They aren't very funny, but some people are a little amused by them because some are very clever.
Hope that helps!