From the Super Mario Wiki
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The Start Dash is a technique that gives runners a boost at the start of a race.
Super Mario Galaxy
At the beginning of a Cosmic Mario or Cosmic Luigi race in Super Mario Galaxy, if the player holds the up, then when the timer hits 2, and then hits just as the race starts, Mario or Luigi will get an extra boost at the beginning of the race. This can be shown by a yellow color appearing on Mario or Luigi, shrinking gradually, showing the end of the speed boost.
Mario & Sonic at the Olympic Games
A Start Dash is a term from Mario & Sonic at the Olympic Games. It is when the racers at the beginning of a "track event" crouch down into their starting position and build up their potential energy to gain a quick boost in their start. In the Wii version, players hold down the button to build up the energy of their character. Once the "GO" sign appears on the screen, releasing the button and swinging the downward will make the racer rocket out of the blocks. When playing the DS version, holding the down on the touch screen will charge up the energy and releasing will activate the speed boost.