The whole point of android is that its the open alternative to apple, so why not open it up? This is the google equivalent of the always popular iPod "Jailbreak".
Rooting your phone allows you to do far more stuff with it:
- install "recovery" which allows you to backup your phones current state to SD card and restore it if installing something breaks it
- install custom firmware ROMs which give better functionality e.g. newer versions of android, added tools/options, themes, overclocking of the CPU, etc.
- Custom firmware also allows apps to be installed on SD card memory, reducing the space usage on your phones internal memory.