Why does a pulsar star pulse?
It is spinning
A pulsar pulses because it is spinning at a really high rate. In fact if you were standing on the fastest spinning pulsar you would be moving at about 1/10 the speed of light.
A pulsar emits beams of electromagnetic energy in one direction (from it's magnetic poles) due to the magnetic field. The point that the beam emits from is not the axis of the spin so the beam is not always pointing at the same spot. In this manner it seems like the pulsar is pulsing.
This picture is a good representation.