Single Phase AC motors generally have ZERO starting Torque. This creates obviously problems. So most single phase motors have a 2nd winding that is used to start the motor. The Start Capacitor
creates a phase delay, so in effect when engaged, the motor is running on two phase AC, which solves the starting torque problem. Once the motor is actually running, the start winding and start capacitor
are no longer needed, so usually there is a current relay (it drops out when the current on the main winding falls off once the motor has started), or a centrifugal switch, which disconnects the start capacitor once the motor reaches a certain RPM, indicating that it has in fact started.
A Run Capacitor serves the same purpose, except that it remains in the circuit at all times, in effect making your single phase motor a two phase motor. This usually results in higher torque, and higher efficiency, or in some cases, lower cost because you can dispense with the start relay/switch. These capacitors (as well as start capacitors) generally handle a fairly healthy amount of energy, so unless they are substantially overdesigned, they tend not to have long uneventful lives. Part of the overdesign is to design them significantly higher voltages than nominal line voltage. The act of closing the switch on a large motor creates fairly hefty transients that for brief periods can be substantially hoigher than the nominal line voltage.
HIgher microfarads means increased current in the start winding, which usually means higher starting torque (and possible shorter start winding life).