Similar to iOS jailbreak you can hack your stock android install to get root user privilege on the device granting you complete control over it. This process known as "rooting" allows users to overcome limitations, add functionality and customize each and every aspect of the operating-system. Compared to iOS jailbreaking, rooting android is a bit easy and can be achieved either by using a desktop application or an application downloaded from market/SD card. While there is quite a fleet of different android powered devices the methods shared below should work on most cases.
If you want to go the "On device" method z4root is the answer, you simply grab the application from "android market" (or download apk to your device storage from computer) and launch it following on-screen instructions.