A brokered convention is one where no one has the 1,237 delegates (Republican Party) to get the nomination on the first ballot. The nomination does not go to the person with the most delegates; you must have 50% plus one.
There has not been one since the 1952 Democratic Convention. There were 16 men who had delegates, but no one with the required number of 616. Estes Kefauver of Tennessee had 300.5. After three ballots and switches, Adlai Stevenson II reached the magic number. Problem was that he met Ike in the next round. He did come back again in 1956 and lost again.