The wastegate only deals with the exhaust side of the turbo. It lets exhaust out of the engine but bypassing the turbo (to control how fast the turbo spins).
When you let off the gas, the throttle blades slam shut but the turbo is still spinning, pushing air out. It has nowhere to go but back out the intake. The pressurized air being forced back through the turbo (aka "turbo flutter") is the same sort of thing as blowing into a window fan. When you're talking about those amounts of pressure against a turbo like that, it can eventually damage the turbo.
A blow-off valve goes between the turbo and the throttle body. It has a vac line attached to the intake manifold. When it sees pressure on the turbo side and vacuum on the intake side (i.e. turbo spinning but throttle closed), it vents out the extra pressure to the atmosphere so it doesn't have to be forced out the intake tubing. This puts less strain on our turbos, and causes less lag in on-off-on situations (more helpful in a stick where you're on and off the gas to shift).
So yeah, what he said. You probably broke something in your turbo...
