What does -10 mean on a betting line?

A team that is listed as -10 is a 10-point favorite to win that game that day. 

If the Dallas Cowboys are -10 against the Washington Redskins and you bet the Cowboys they must win by more than 10 points for you to win your bet.

So if the final score is Dallas 28, Washington 14, you win. If the final score is Dallas 28, Washington 21, you lose. And if the final score is Dallas 31, Washington 21, the game is a push and you break even with your bet.