The distributor speed is not affected by the amount of vacuum coming from the manifold. Its relative phase in the compression/fire cycle is affected.
The consequence is that the vacuum in the manifold rotates the rotor a relative amount via a mechanical linkage, and changes where in the cycle the spark ignites the petrol.
This has the effect of increasing the amount of torque and power that the engine generates.
Timing advance and retard is a slightly complex subject which needs to be understood if you wish to tune your own car.