Someone explain these cards, please, in words a simple mind like mine can understand
For a truly simple mind, I would suggest: Don't Bother
For the more general purpose:
1) You get cards by playing games marked as having cards; the cards are given to you simply based on time playing the game, not related at all to achievements or whatever. You can only get a certain number of cards from a particular game before they stop dropping.
2) If you get a set of cards you can craft them into badges, which iirc also lets you get new profile backgrounds, emoticons, etc.
3) If you don't care about collecting the cards (I'm guessing you personally would not) you can trade them to other people for whatever or put them up on the steam marketplace (if it sells you get credited in steam-wallet money).