Partial sends are intended to be used with effect racks and allow peeling of a percentage of the output audio signal from one rack and sending it to another. In this situation, a single plugin (or series of plugins) can be used to apply an effect to the output of multiple racks. It saves on CPU load since all the partial sends are mixed and then processed once.
Each rack supports up to two partial sends:

The two knobs on each rack slot are used to control the send amount.

The partial send amount can be controlled with the on-screen knob, though MIDI controller assignments and by sub-sessions.
Partial sends are available Cantabile Performer edition only.