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When a motor runs it also acts as a generator, generating voltage opposite to the applied voltage. This is known as Counter ElectroMotive Force (CEMF) because it opposes the ElectroMotive Force (EMF, AKA voltage) that is applied to the motor.

A given motor under a given load will have a running current determined by the difference between the EMF and CEMF. If the load increases and the motor slows down the CEMF will also go down allowing more current to go through the motor.

When the motor is stopped there is no CEMF so the current going to the motor is at maximum for the applied voltage, limited only by the resistance (reactance) of the motor windings until the motor starts turning. To add torque to a single phase AC motor starter windings are used that are off-set from the run windings by some angle. To create a rotating magnetic field the voltage applied to these windings must be out of phase with the voltage applied to the run windings. This is generally accomplished by a starting capacitor which is only in the circuit up to a certain RPM.

The larger the starting capacitor, the more phase difference between the windings which generates more torque and lowering the time and amount of starting current (to a point). That is your simple hard start capacitor.

The "soft start" or easy start kit includes the capacitor as well as a voltage ramping circuit that limits the voltage applied to the motor as it is starting which limits the starting current.

That's your simplified AC motor theory for today. I hope it helps.