The card game is by Looney Labs and you can find more info on it
here.
The game features a really fun system where you must affect certain key moments in the BTTF timeline (which covers all three films) and the changes you make ripple across other years.
You play as a descendant of Marty, Doc, Biff, and others, and you are trying to set the timeline to "your" version so that you aren't erased from existence. Once you do that, you have to stop 1955 Doc from falling off his sink while hanging the clock, thus un-inventing time travel (which is actually a huge paradox, but whatever).
I heartily recommend this game. It's fun, fast, and crazy. There are tons of in-game references to the trilogy and the game is easy to learn.