An act of spite is something that you wouldn't ordinarily do, just to prove a point and get back at someone who pissed you off. The spiteful act can be something out of character, something you don't enjoy doing, or even something that hurts you. You rationalize this by knowing that even though you might be hurting yourself, the satsifaction you'll get from pissing off the other person will more than make up for it.
If the QB is being a dick to the offensive line, they can step aside out of spite, and let the linebackers sack the QB's ass. They'll sacrifice the play and could lose the game if the QB gets injured, but it's worth it to see the QB get fucked up.
You're boss offers you a promotion, but everyone knows that if you decline, he'll offer it to your coworker. You might not even want the promotion, but if your co-worker is being a douche, you can take the job out of spite, just to piss him/her off.