This expression comes from the game of FOOTBALL, where it's not a good thing to drop the ball when the ball is in play. It's mainly used based on failure and mistakes. So, if you want to tell someone how important it is to succeed in a particular activity, then this is a good expression to use.
Someone fucking something up because they're incompentent or weren't paying attention, thusly fucking themselves and possibly others over.
Biff: Christy sure dropped the ball on this whole Christmas party thing, now I have to come in this Saturday to help decorate.
Joey: That blows dude, she should be fired.