Apple has the App Store, jailbreakers have the Cydia Store in addition to the default App Store. And if you want to be technical, Cydia was THE first App Store. It was available with iOS 1.x and allowed jailbreakers to download apps before the App Store even existed. Those who jailbroke their first generation iPhones on 1.x have seen several jailbreak ideas and concepts become parts of iOS. We would mention the other Jailbreak App Store, Rock, but seeing as Cydia acquired Rock, there's probably no point now.
Another term you may hear when it comes to Cydia is repos, or repositories. These are simply sources you add in the manage section. ModMyi and BigBoss are two of the largest. They are already added when you install Cydia. You are always welcome to add custom repos if you choose. I highly advise only adding repos from trusted sources. If you have a weird feeling about adding it, I'd probably pass.