One of the many new coinings that begin in sport and then cross over to other contexts, three-peat is a portmanteau word, a blend of three and repeat. Quite simply, it means winning a championship, race or other competition three times. If they are consecutive wins, even better.
Lydia Ko gets the three-peat, winning the Sticky Bunker Golf Championship for the third year running!
The backstory to this term is that it was registered as a trademark in 1989 by the coach of the Lakers basketball team. There have been several legal challenges to this on the grounds that the word is too generic (too much in everyday use as a noun describing a general state or situation) to qualify as a trademark but so far, its status remains.
Rap singers and the more creative have shifted three-peat over to other achievements like having sex with three different people in the same day/night/weekend/week (You choose when you use it!)