When you're using public key encryption, it's important to be sure that the key you use to encrypt a message really belongs to the recipient (see key verification). PGP makes this a little easier by having a way to tell others "I believe this key belongs to this person -- and if you trust me, you should believe that too." Telling the world that you trust someone's key is called "signing their key": it means anyone who uses that key can see you vouched for it. To encourage everyone to check and sign each others keys, PGP users organize key-signing parties. They're almost, but not quite, as exciting as they sound.
Analogy: It's like a networking party, where you introduce your friends to other friends.