Most directly put, the study of how to put a bracket together. Popularized by the NCAA Men's Basketball Tournament, bracketology is the system by which sports analysts and the NCAA committee decide, by a series of statistics such as RPI, win-loss ratio, final AP Ranking, and auto-bids decided by the outcome of a teams regional end-of-season tournament, what 65 teams (including the play-in game for the two least-qualified team) will play for the chance to win the NCAA Div. 1 Men's Basketball title. Teams are separated into four regions with 16 teams placed in each region. Each region contains teams with seeds #1-#16 and tournament play commences in early-mid March, hence the dubbed tournament name, March Madness.
Bracketology is not limited to the NCAA Men's Basketball tournament, but that is the most common usage of the term when referred to in sports.
After brackets are set up by way of bracketology, the 65 team tournament field, a team must put together a series of six wins against some of the best teams in the country in order to win the prestigious NCAA Title.