unlocking the root directory of the phone so that you can edit its content, as such to change parts of the software or to even replace the whole operating system. Android is an open source OS, so if you have root access, you can install a custom version of the operating system, instead of using the default software. It can also allow you to change settings in the phone to change its hardware performance.
The reason I rooted my phone is a good as example as to why its beneficial to root your phone. I rooted mine because my G1 had no official updates after 1.6, this limited my access and ability to run many apps available on android. I install a custom rom and now my G1 runs Android 2.2 giving me more access to software and other functions my phone can perform.
Similar processes can be done to unlock Iphones, Ipods and Ipads, and also various games console such as 360s and old xbox, Ps3s and PSPs. I thank there is custom firmware for Nintendo DS aswell.