A "game changer" is a slang term, of relatively recent usage, usually applied to politics. I first heard the term used in the 2008 election, and there was a successful book written about that election called "Game Change".
As the term suggests, a "game changer" is something that...changes the game, with the "game" usually being an electoral contest, although it can of course be applied to any type of contest or movement. More specifically, it is something unexpected and major, that changes things not just in quantity but in quality. A "game changer" is something that changes the parameter of a political contest. For example, a candidate that manages to attract a demographic group, or who has a very organized approach to campaigning, can be considered a game changer. Many or most game changers are negative, however: a gaffe, an old scandal, or an October Surprise. The 2008 election was famous for seeing many game changers: the sophistication of Barack Obama's campaign and his demographic appeal, the surprise pick of Sarah Palin as John McCain's running mate, then her subsequent troubles, and the stock market crash a few weeks before election day.
But as is often the case, the term "game changer" is often overused. Most political campaigns are not wildly dramatic rollercoasters: they are instead, fairly predictable, which is why true game changers are so noteworthy when they do happen. But for dedicated campaign watchers, small events take on large dimensions. A stutter during an interview or a bad poll number, which will be forgotten by the general electorate in a few days, is often trumpeted as a "Game Changer" by the punditry.