Since induction motors have inherently low power factor, 
Capacitors are used to improve the power factor. In 
fractional hp motors, they are used in the starting winding 
to temporarily convert the motor into 2ph motor to make it 
self starting

Capacitor provides the starting torque & also improves the
power factor of the induction motors As they have low power
factor

To improve the power factor of the motor. motor is inductive
load it draw reactive power from system.so we have
compensate the reactive power component from capacitor.for
single phase motor capacitor used for stating purpose
also.and single phase motor are low power factor motor
because due to large air gap B/W stator and rotor so it draw
more  current from system.so capacitor are use in induction
motor