if it's updated to 3.1, i'd be surprised if the jailbreak will still work. cydia may be installed, but until you try to download something off of it we won't know that it still works. reason i say that is because the release of 3.1 has rendered most JB's useless until the DevTeam releases their update.
but to answer your question, Cydia is an 'app store' for JB. it has apps that provide different features/enhancements for your iPhone, it has apps, it has themes, wallpapers, etc, etc. play around on it and you'll soon see what all it has to offer.
that's why i'm still on OS 3.0.1 so that i can keep my JB functional.