The Pulse effect is one step above a Set Level. In fact this effect can do everything the Set Level can plus more. The main differences here are the ability to use a color gradient over a single color and the ability to shape the brightness as a curve value to vary over the length of the effect. See the sections on Curves and Color Gradients for more details on how they work.
With the ability to control the brightness over the duration of the effect, the Pulse enables things like a fade on or fade off by adjusting the curve from a ramp up or ramp down. But the curve can take any shape and thus you can form your pulse to do about anything.
The pulse is also highly useful as a modifying effect when using layers. It can be used to fade other effects on or off, or control their brightness. See the sections on Layers for more details.