A Mulligan, in a game, happens when a player gets a second chance to perform a certain move or action; usually due to lack of skill or bitter luck. A "Do-Over". Like getting an "Extra Play" in pinball due to sinking the ball before obtaining an arbitrary amount of points.
If your opening hand in Magic: The Gathering sucks bad; just call "Mulligan", reshuffle, and draw new cards.
When a dating relationship is brutally derailed by submerged emotional issues unknown to either person. If the derailer is allowed a second chance by the derailed, its a Mulligan. Even more so it accompanied by a decent bitch slap.
Wes: Dude, I can't believe all this time I didn't realize I was a sad bastard with ungodly sorrow, projecting my emotional issues on you! Please bitch slap my issues back into my subconscious and give me a Mulligan.
Laura: Fine. Take me to a nice restaurant on Friday night and it'll be fine...SMACK!