Motors require both magnetizing (reactive) current and load (active) current. The active current supplies the motor the power to do the work, and the reactive current establishes and sustains the magnetic field that allows the motor to spin. Reactive current is constant and does not vary with load. It does not consume energy because its sine wave lags the voltage's sine wave by 90 degrees.
The problem is simple. The reactive current, while necessary, doesn't consume energy but adds to the total current supplied by the utility company. This can be a hassle for utility companies since they are required to provide the infrastructure to supply the reactive current but cannot charge for its energy consumption. When it becomes too much of a hassle, they slap you with penalties. If the reactive current can be supplied without sending it down the cable, then the cable and other related infrastructure would only need to be sized to deliver the active current.
A capacitor system accomplishes this goal. When the motors magnetic field builds up, it demands reactive current. A capacitor releases the necessary reactive current. On the flip side, when the magnetic field is collapsing and kicking current back into the system, the capacitor is absorbing the current and building a charge. The main result is that the capacitor allows the motor to draw significantly less current from the utility company (see Figure 1).
For a more detailed explanation of the work of capacitors in power factor correction, take a look at the MZI Application Guide for Power Factor Correction