The processor (whether its a CPU or a GPU) or memory (RAM) has a certain clock speed,or frequency, measured in Hz, that it operates at. Basically, the higher the clock speed, the more stuff it does in one second. When you overclock a processor, you send more wattage to the chip. When you do that, it increases the clock speed of the processor beyond what is was built to do. This ends up making the processor faster, but the trade-off is that the processor generates more heat. Also, the second you overclock (at least with most hardware) you void your warranty and any damage done to the hardware after that, the manufacturer will not replace.
Overclock too much, and you might end up damaging your hardware. But if you keep the chip cool, probably by using an aftermarket cooler, you should be safe. Most overclocks aren't incredibly huge. For instance, if an overclocker has a CPU with a base frequency of 3.5 GHz, he might overclock it to 4.0 GHz. Some people go as far as 4.3 GHz, and some even up to 4.7. Some extreme OCers go as far as 7 GHz.