The ballast regulates the amount of power the fluorescent light receives. The voltage when turning on the lamp needs to be higher to light the light, but a lower power is needed to sustain the light. Different types of ballasts control this amount. Dimmable ballasts let the light work at various percentages of the total power going to the light. This creates different light levels with the same fixture. The most common ballasts just switch the light on or off without dimming the light.
Ballasts can be magnetic or electronic. Magnetic ballasts are the older type of ballast, and unless you get an energy-efficient model, the ballast will use more power than an electronic ballast. Electronic ballasts do not have the hum or flicker experienced with older fluorescent lights operating off a magnetic ballast.
Some ballasts are not separate from the light. Screw-in compact fluorescent light bulbs have the ballast built into the base of the bulb. This is why the base of these bulbs is longer than it is in incandescent light bulbs. Even if you can't see the ballast, you still need one for the fluorescent light to work.
Some ballasts are rated to turn on more than one fluorescent light. Two of the most commonly used ballast types, T-12 and T-8, can operate up to three lights for the T-12 or up to four lights for the T-8. Groupings of four fluorescent lights in a fixture can be operated with a single T-8 ballast, if needed, so you will not always need a ballast for each light.