From the Super Mario Wiki
Synchronized Swimming is a real-life Olympic event that can be played in Mario & Sonic at the London 2012 Olympic Games. It is under the "Aquatics" category, along with 100m Freestyle. The goal is to perform a pool dance routine by posing.
In this event, teams of 4 compete for the most points with their pool performance.
This game uses only the Wii Remote. The player watches for pictures to appear onscreen, and poses with them when the remote hits the picture. If it is a pose, the player must swing the remote in the exact direction. If it's a mark with rhythm, the remote has to be swung around. If it's a spin, the remote has to be spun around.
There are three songs to choose from which are Spring Song, Trisch-Tracth-Polka, and Hungarian Dance NO.5, in order of ascending difficulty. The 3DS version, however, has only one song which is not named.