It works very similarly to Agent P, in the sense that you go somewhere in the park and do something there.
When you start your quest (either at the Firehouse on Main Street, or behind the Christmas Shop on Liberty Square), you'll get a pack of cards per guest. You will then be directed to a portal (they'll give you a map and a key to open the portal).
You use your key to open the portal, a clip will show, eventually a bad guy will show up and you have to use your cards (any card will do if this is your first quest) to defeat them. Then you will be directed to another portal. After 3-4 portals you'll defeat the main bad guy (a major Disney Villain), and you'll be directed to another "Land" in Magic Kingdom to start another quest.
I believe there's 8 main villains, and then Hades from Hercules as the last boss.
You get a pack of cards each day you visit the park, and each time you defeat the entire quest (8 villains + Hades). It takes quite a while to do the whole thing though, if your time is limited I'd only do one or two villains.
The cards are collectable, there's 60 cards that can be obtained inside the free packs you get for visiting the park, there's 10 extra cards that can only be found by buying a special pack, and then there are some limited edition cards that are given during special events, like the Christmas and Halloween parties.