Developers (for example: some people on these forums) make applications.
They submit the applications to Apple.
Apple put the applications on the App Store.
iPhone and iPod Touch users download the applications.
If the application costs money, 30% of the money goes to Apple, the other 70% goes to the developer.
Apple pays the developers their share (70%) every month - this is what the developers are referring to when they say "getting paid".
E.g.
Joe Bloggs puts his app on the App Store for 99c
Billy downloads the app.
About 30c goes to Apple.
About 70c goes to Joe Bloggs.
At the end of the month Apple will give Joe Bloggs his 70c