For the definition of pulses, see the entry on Legumes.
Pulse as a kitchen verb may have come into play first with blenders, then with food processors. Before those machines, cooks would have been quite perplexed by directions in the middle of a recipe to stand there and “pulse.”
Pulsing is done by turning the power off and on rapidly. It can be one button for start, another for stop, or it can be one button that you push or release for quick starts and stops. On most food processors, the power for the pulse will only flow as long as you are pressing the pulse button.
Pulsing gives you control over how much the items in the jug are getting processed, and gives you time to see how things are coming, and the ability to call an end to it all in time.
The first food processors didn’t have a pulse button and many food items got overprocessed, with nuts intended to be a nut meal speeding into nut oil.