The first announced feature is achievements, which according to an FAQ, are "designed to incorporate the best aspects from all the existing achievement systems out there (Xbox, PS3, Steam, Battle.net etc etc) and improve upon them and add a Paradoxian quality to them." The rewards will use points and pop-up in game.
Games that support Paradox Achievements will "have you log into a (local) ingame profile when you start the game. You will then have the option to link that profile to your forum account. As you unlock the achievements your new point total will appear in your paradox forum profile."
It is likely that Paradox Connect will be available regardless of where you purchase a supported game. Similar systems, like Ubisoft's Uplay, are available in Steam copies, for example. What Paradox Connect isn't, however, is DRM.
More features should be coming along for the new system and it is scheduled to begin beta testing in Q4 2010.