Funnily enough we recently had a thread about this exact thing. Don’t worry, though, no problem explaining it again.
Basically it is a home run during the home team’s half of the inning that ends the game. If the home team goes into the bottom of the ninth, say, down by a run and someone hits a home run with one runner on the game is over. Doesn’t matter if there are two outs, one out or no outs or what the count was. The visiting team doesn’t get to bat again.
Joe Carter won a World Series for the Toronto Blue Jays in this fashion about ten years ago.
Okay, to be specific: the batter trots around the bases (in rare instances with one flap down); any other baserunners do likewise and may wait for the batter around home plate; other members of his or her team may come out of the dugout as well; the pitcher may turn and watch it go, uttering profanities, or may hang his head for a moment before walking off; the rest of the defense walks off the field. Is that better?
ESPN.com did a piece on the phrase a couple of years ago when it suddenly became popular. Call it 2001 or so.
Prior to that I’ve always heard them called ‘game ending’ or ‘game winning’ home runs. I feel certain some sportscaster somewhere coined it and the meme worked it’s viral way around because it sounds good.
I’ve always heard Dennis Eckersley credited with having coined the term in the early 90’s. ESPN definitely took it to obscene proportions sometime in the last couple of years, though.