The Sakurai angle is a special knockback angle programmed into certain attacks. While it reads in the game data as an angle of 361 degrees, the game treats it rather differently. On a character with no damage, it is approximately an angle of 20 degrees. But as damage increases, the angle also increases to about 40 degrees.
The angle's name is derived from the fact that it has a chance of tripping up to the point where the target starts tumbling from the knockback. As Masahiro Sakurai is sort of hated for making tripping existent in Brawl, it is hence named after him.