A wastegate is a device employed in cars using a turbocharger. Basically a turbocharger operates by utilizing the pressure from the engine exhaust to power a compressor at the engine intake, increasing the amount of a air in the engine at detonation.
Without a wastegate all the engine exhaust would pass through the drive side of the turbocharger. The wastegate provides an alternative path for exhaust, bypassing the drive side of the turbocharger.