It's often been said that there are probably more crashes from riders losing the front end in a corner than from overstepping rear tire traction and highsiding on the exit. The reason is that a motorcycle is made to function at its best under power; the inherent design of its chassis and suspension means that the machine is much more stable when power is applied. Anyone who has hit a false neutral in midcorner will tell you how difficult it is to control the bike when it's not under its own propulsion.
This is why it's good practice to cut down your "coasting" time, such as during the transition between braking and getting back on the gas. A motorcycle isn't as stable when you're braking hard, which is why it takes up so much of your concentration when you're entering a corner. Especially in tighter sections, like hairpins; some riders often end up not opening the throttle until they reach the apex because they're so concerned with the bike's stability up to that point
As you approach a corner and have accomplished the majority of your hardest braking (usually while as upright as possible), you begin to ease off the brakes in preparation for your corner entry. Because you must balance the front tire traction between braking and cornering forces (obviously you can't use 100 percent of the front brakes' power while leaned over), you begin to gradually let off the brake as you increase your lean angle.
It's at that point, where you completely let off the brakes, that you should "crack" the throttle open as soon as possible. You don't need a handful of throttle; just a small enough opening to get the engine off idle and transmitting power to the rear wheel. It needs to be done carefully because you're often at a pretty severe lean angle by this time, and opening the throttle too much (or if your bike has an abrupt off/on throttle response) can upset the chassis at a critical area in the corner.
Once you get some power applied to the rear tire, you'll be amazed at how much more control you have over the motorcycle. Because you've now transferred the bike's weight to the rear, the steering suddenly becomes lighter, and you can choose a corner entry line (and stick to it) with far less effort. The suspension and handling also become much more settled, since the front fork and tire aren't being asked to support the weight of the whole motorcycle/rider combination.
But the biggest benefit of getting on the throttle as early as possible? You can begin your drive out of the corner earlier, which obviously pays dividends in added speed down the next straight. The additional corner speed is more momentum you can use to the next bend. There's a saying among racers that you want to "use the brakes as little as possible"-use the brakes hard and quick, then get off them as quickly as possible so that you can get on with the business of accelerating, which is where time is made.
It's important to note that any time you are not on the throttle, your bike's weight is biased toward the front. And if you are at a very extreme lean angle (with a correspondingly small and tenuous contact patch), overloading the front tire will obviously have dire consequences. Any racer will tell you that it's a lot easier to save a rear-end slide than a front-end slide. Even cracking the throttle open just a bit is enough to take that weight off the front tire, giving you an added margin of traction and safety when you need it most. A good example would be if you were recovering from overshooting a corner; as you use up every bit of lean angle to keep the bike on the pavement, your chances of not losing the front are better if you just crack the throttle open a bit to get some weight off the heavily loaded front tire.
The old humorous adage, "When in doubt, gassit!" may seem like a nonsensical act, but it actually has some merit-in a much more controlled fashion, of course.