The Sweet Sixteen in March Madness is the Round of 16 teams, in which the winner from pod one faces the winner from pod two, and the winner from pod three faces the winner from pod four, in all four regions.
First and foremost, a team must qualify for the tournament. There are 68 teams fighting for 16 spots in the Sweet Sixteen. If a team plays in the First Four, they must win their game to advance to the Round of 64. From there, a team must win two more games to make the Sweet Sixteen. Put simply, a team must win either two, or three games (if in the First Four) at the start of the tournament to get to this round. It is special because it marks the halfway point of the tournament. If a team wins in the Sweet Sixteen, they only need to win two more games to make it to the National Championship.
The Sweet Sixteen is the Regional Semifinals, and within each region there are four teams left standing going into this round. Teams which are victorious in the Sweet Sixteen advance to the Elite Eight, which is the Regional Championships.
A Cinderella story occurs when a team ranked 11th or worse in any given region advances to the Sweet Sixteen or further. There is usually one Cinderella story each year, and it will likely get a lot of media coverage. Not to mention, it will leave thousands of fans' brackets in shambles.