Primaries don't elect candidates; they elect delegates. The goal of this whole thing is to get 1,144 delegates at the Republican National Convention, to be held in Tampa, FL in August. Each state gets so many delegates at the convention, and each primary/caucus decides who each delegate is sworn to vote for. But the delegate's obligation is only for the first vote at the convention. If no candidate reaches the 1,144/50% threshold, then all delegates are free to vote for whomever they please for the remainder of the convention. Voting continues until one candidate gets a majority.
Here's the thing: the delegates can vote for whomever they damn well please. They can vote for any eligible American. ANY! They could vote for Jeb Bush, or Brad Pitt, or my mother, or ANYONE!
Usually, each state's Republican Party chair attempts to control his delegates' votes by making various promises to the delegates, such as party support in future elections. Each candidate attempts to make deals with other candidates; e.g., Ron Paul would offer his, say, 300 delegates to Romney in exchange for a promise to return to the gold standard, and if he's able to actually deliver those 300 votes, he might put Romney over the 1,144 threshold. So a brokered convention can devolve into influence-peddling, with the expressed will of the voters rendered essentially irrelevant after the first ballot.
Next time, we'll discuss why/how a brokered convention could happen, and also why it probably won't.