The sympathetic nervous system regulates your body into a fight or flight response–increasing your heart rate, breathing, etc, upon registering the affects of an outside stimulus. In this case, what you’re asking deals with that stimulus being exercise of the body itself.

When you move your muscles excessively overtime, the sympathetic nervous system responds and makes note that more oxygenated blood is needed to produce energy in your system to keep you going. Increase in breathing and in turn, heart rate, all aid to that need. Your pulse is determined directly by your heart, which is just the movement of your vessels (primarily arteries) which move in the first place because of the pressure of blood exerted on their interior walls from your heart pumping it through.

An increase in heart rate directly equals an increase in one’ pulse rate because the harder and faster your heart beats blood through your vessels, the harder and faster the blood will pound at the walls of those vessels, creating a change in the pulse.
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The blood gets pumped and cause a pulse which you can feel on your wrist or neck by either the Artery, or vein.

And that, is why.
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