When it comes to grow lights and other electronic devices, a ballast is mechanism that acts as a type of resistor. Similar to the "power pack" used with electric trains, its purpose is to regulate the amount of electrical current flowing through a circuit.
If grow lights - such as metal halide, high pressure sodium or even fluorescent lights - were connected directly to a power outlet, they would continue to draw greater and greater amounts of electric current until they burned up, exploded, or destroyed the power source. This is why a ballast is necessary. The ballast provides positive resistance which limits the flow of electricity to the lamp.
Traditionally, the ballasts used with grow lights have been similar to those found in old-time automotive ignition systems, i.e. a magnetic coil. The problem with these is that they were designed to build up a certain amount of electrical current required to operate the light; once this level was reached, the power would be delivered to the cold bulb all at once. This caused a great deal of wear on the bulb mechanism, shortening its useful life by a substantial degree.
The other problem involved "strobing," or flickering. This flickering is not normally perceived consciously by human eyes, but it does exist - and again, causes grow-light bulbs to be less efficient.
New digital ballasts address these problems. First of all, electrical current is not fired off to cold bulbs all at once; instead, these ballasts start off by sending low levels of current to the bulb, then increasing the amount as the bulb warms up (known as "soft starting"). Digital ballasts also provide a smooth, even flow of electrical current, unlike magnetic core ballasts which cycle. This eliminates the destructive strobing action that causes bulbs to wear prematurely.
Another great feature of the digital ballast is that it is "intelligent." Different types of grow lights have different power needs. In the past, it was necessary to have different ballasts for metal halide and HPS lamps, or at best, use a special (and often expensive) ballast that had a switch allowing one to change bulbs.
Today's digital ballast is optimized to distinguish between different types of grow lights and adjust its output accordingly.
The result is that grow bulbs are effective over twice as long as those powered by a magnetic coil ballast.
This said, it should be noted that not all digital ballasts are created equal. These can vary tremendously in terms of quality and effectiveness. Some digital ballasts can actually harm your plants by delivering insufficient current to the bulb, limiting its ability to emit light.
On the other hand, whereas the performance of coil ballasts starts to degrade after about three years, digital ballasts do not.
If you are considering the purchase of a digital ballast, it is a good idea to do some comparison shopping, and be prepared to spend a bit extra; a new, but cheaply made imported digital ballast from China might be worse than even an old coil ballast made in the U.S.