Rooting is a process to enable one to have unrestricted full access to the Android stack . It is similar to the access of an Administrator on a Windows based computer.
Having a rooted phone gives the end user unprecedented control over the phone, enabling one to have unlimited possibilities to increase the phone's full potential. One can alter system files and can replace many parts of the Android Core ( themes, core apps , recovery image, bootloader, boot images, etc ). With root/superuser access on the phone, one would be able to flash modified roms (roms from other devices) , have access to certain functions on "root only" applications (example: wireless tether for root users - ability to tether your phone). With some cooked rooms - one can installed applications and relocate (browser/maps/market) cache to the sdcard
There are many risks associated with rooting your phone. The most apparent risk is bricking your device - meaning making your phone useless and end up as just a expensive paperweight. Bricking is when you are unable to enter recovery, fastboot, or your rom, and your device is stuck on the splash screen indefinitely.
Major disadvantages of rooting : warranty is void and one is unable to have over the air updates. Any updates had to be done manually thro recovery by flashing the relevant update zip file
These are some of the popular Android smartphones and links on HOW-TO root is listed :
Sony Xperia X10
HTC Legend :
A very comprehensive guide and tutorial on Rooting :