A brokered convention happens when no single candidate has a majority (51 percent) of delegates during the first round of balloting. Even if Donald Trump wins more delegates than any other candidate, if he doesn't hit that magic number (1,237) on the first round, there'll be a second ballot.
That's where things can get interesting.
A fun read on what a brokered convention is, how it actually used to be the norm and why it could happen in 2016. Yet another great explainer by Vox.