The wastegate is the standard method for limiting boost to a certain level in a turbo setup. It's mounted either to the exhaust manifold before the turbine housing (external) or to the turbine housing itself (internal). It has a vacuum line plumbed from the intake manifold, and a dump pipe that runs from the wastegate to the downpipe after the turbo (or sometimes out into the atmosphere, but this isn't emissions-legal). There's a spring inside the wastegate that gets pushed on by boost pressure inside the vacuum line. The spring is connected to a valve in the wastegate which routes some exhaust gasses around the turbocharger and prevents it from spooling any higher. The more boost you have, the more the valve opens. The pressure at which the wastegate opens all the way can be changed by changing the spring to either a stiffer one for more boost, or a softer one for less boost.

All boost controllers place some kind of restriction in the vacuum line between the intake manifold and the wastegate, which allows you to change the boost pressure at which the wastegate opens. Basically the boost controller (mechanical or electronic, doesn't matter which one) prevents the wastegate from seeing any boost. When the boost level you have picked is reached, the controller opens up the valve all the way which lets the wastegate see the full boost level all at once. Generally this is higher that whatever boost level the wastegate spring provides so the wastegate opens right up. This way, the wastegate stays closed all the time until you reach max boost instead of always bleeding off some exhaust gasses. This tends to help spool-up because the wastegate is forced to open in an on/off fashion rather than progressively opening depending on how much boost pressure there is.