Cards are just collectibles you can receive for playing most games. Their distribution isn't uniform: some games you'll need to play for a while as single cards are handed out per hour or so. Other cards you appear to receive fairly immediately.
Each card is part of a set, you woo't be given the full set, that you can then trade others for or simply buy the rest yourself. Each card tends to be 'round ten cents. The purpose of the sets (and I went a li'l crazy with five dollars) is to get them, turn them in and receive nifty items in return. Background screens for your profile, personalized emotes, other collectibles. Also, I've received two coupons for games.
The cards/sets are nothing more than bragging rights, really.
Also, I purchased Rebellion at full price (you're welcome, Stardock). It's sorta-kinda worth it. 'Ish.
I need stop playing the huge and vast maps. It'll probably make the end game more exciting.