This phrase is used in sports betting to describe an event late in a game which enables the underdog to cover the point spread.
The underdog in any given sporting event is the team expected to lose a game. However, in sports gambling, each game has a betting line. The betting line typically gives the underdog a certain number of points, also known as the spread. So if the New York Yankees are favored to win over the Boston Red Sox by 6 runs, the spread is 6 points. If the Yankees win by 7 runs or more, individuals who bet on the Yankees win their bets, while those that bet on the Red sox will lose their bets. However, if the Red Sox score in the 9th inning only loses by 5 runs, those who bet on them will win their bet. This is what is known as a back door cover because the Red Sox covered the spread.