Boost refers to the pressure generated in the intake manifold by a turbocharger.
All things being equal, more boost forces more oxygen into the engine, which allows it to burn more fuel and thus more power, but in practice all things don’t necessarily stay equal. As RPM and boost increase, turbo efficiency may decline, causing the turbocharger to blow hotter air. Hot air is less dense, thus contains less oxygen. Hot intake air also makes the engine more prone to detonation.