A Mulligan is a do-over in golf, when a player gets the opportunity to replay a stroke. However this is not a rule that is allowed in competitive play like official competitions. It happens more often in social golfing, when a player is new to the game or has a particularly bad opening shot, they will be offered the option of a "do-over" by their fellow players.

This term has been adopted into other games as well, especially when someone is new to the game and trying it out. In darts for instance if someone's first throw is particularly bad or does not even reach the board, the player might get a another attempt - a do-over.

According to PGA records, David Bernard Mulligan (a prominent amateur golfer, playing at Winged Foot in Mamaroneck, N.Y. Golf Club), sometime between the late 1920s and mid-1930s, was provoked by a terrible first shot off the tee, he put down a second ball to take another shot. His perplexed playing partners enquired what he was doing, and he replied with ‘I’m taking a correction shot,'. They asked him what that rule is called and he simply replied 'a Mulligan'.

The practice soon spread, with it the name.

More Info: en.wikipedia.org