About Steam summer sale badge

You get cards by purchasing games within the Summer Sale.
You can trade them and buy/sell them on the Community Market.
If you have the complete set, you can craft the badge and level it up.

Normally, when you craft a badge, you get an emoticon, a profile background, and a coupon.
Before the summer/winter sale starts and until it ends (so for a 2-4 week period), you get an event card instead of a coupon. These event cards are tied to the specific summer or winter sale. These cards can be collected into badges as well, like normal game cards. The badges usually need 10 cards, and unlike the normal game badges, they have infinite levels (no capping at level 5 or level 1 foil).

This is why many, many people postpone crafting badges until these events start, since they get a card for doing so instead of a coupon.
The downside is that the event cards have a limited life span: when the sale ends or shortly after, they turn unmarketable and can eventually disappear if you didn't sell or use them up.

Unanswered questions of yours; it doesn't have a level limit which some craft to 1000x levels. Also there are 2 other ways to acquire sale cards other than crafting badges; every $10 total purchase of games gives 1 card (Steam keeps track of your purchases during sale) and there is always an Steam event during sales which grants free cards if you participate in it.

My wallet says "hey man."

"I'm here to do favors and kick ass, and I'm all out of favors."

Then it's on.