Synaesthesia is commonly known in the medical world as a condition in which people hear colors as specific sounds when they see them. In the gaming world, it's a design choice in which visuals, user input, and sound are all fused together in one amalgamation of a sensory overload.
As the most commonly cited example, Rez
is basically the foundation for which all modern synaesthetic games are based. The game is played like any other on-rails shooter, but all the sound effects & visuals in the game are synchronized with the beat to the music, and tonally & sonically crafted to become a complement to the song. This gives the effect of the user basically creating a song as they play the game normally, as opposed to a rhythm game where playing a song is the entire purpose, and failure results in dischordance. Failure in a synaesthesia game simply results in a less complex song.
Tetsuya Mizuguchi is famous for pioneering this genre, and later went on to apply the design philosophy to the Tetris
-like "falling block puzzle" genre with Lumines
. Since his creation of Rez, many more games have popped up with this concept as a main attraction, such as Space Invaders Extreme.