Wastegate
A wastegate is a device that bleeds off excess exhaust gasses before entering the turbine of a turbocharger, to maintain a certain boost pressure produced by the turbocharger. By controlling the amount of exhaust gas released through the wastegate (and thus, diverted from entering the turbine), wastegates help maintain a certain desired boost pressure level produced by the turbocharger.
Types of Wastegates
Most vehicles that come turbocharged from the factory use internal wastegates. This means that the wastegate is integrated into the exhaust side of the turbocharger itself. This is usually done for cost and/or simplicity. Some feel that the design of internal wastegates can be limiting for high performance, but most feel that it can be made "good enough" for almost all applications.
Internal wastegates use a pneumatic actuator that swings the wastegate door open, as shown below.
External wastegates use pneumatic valves (essentially the "door" and actuator all in one unit) mounted before the turbocharger on the exhaust manifold. This allows the engine builder to design a larger, more efficient route for the exhaust gas to escape, often yielding improved performance, but at the expense of higher cost and complexity, and physical size.