How do Electronic Ballasts in Fluorescent lights work ?

A Ballast in a fluorescent light is necessary to get the light glowing.  The Ballasts generates a high voltage by means of the would coil which acts as an inductance.  When the starter interrupts the supply to the inductance, a powerful voltage is generated.  These are called magnetic ballasts. 

However, magnetic ballasts take time to get the lamps to start.  They also have an undesirable hum.  They also produce a flicker before the tube lights up continually.

Electronic eliminate the problem of initial flicker and hum.  They also reduce power consumption.
Electronic Ballasts work by converting the AC supply into DC first.  This rectified DC is then chopped by a chopper circuit to generate high voltages to start the discharge in the lamp.  The chopped AC waveform is t a very high frequency of the order of kHz.  This ensures that the flicker is reduced to a minimum.

The efficiency of the lamp is also increased.  Electronic Ballasts are 10% more efficient than magnetic ballasts. Electronic Ballasts can generate harmonics.  This, however, is insignificant as the amount is very small.