There is an external card on the s3 mini - well there is on mine anyway. Rooting is allowing you total access to change anything on the phone. It takes about ten min to do and then you can change anything you want and can install whatever you want. You can also wipe all the shit apps like 'chat on' that the manufacturers put on and can't normally be removed.

From Wikipedia:
Rooting is often performed with the goal of overcoming limitations that carriers and hardware manufacturers put on some devices, resulting in the ability to alter or replace system applications and settings, run specialized apps that require administrator-level permissions, or perform other operations that are otherwise inaccessible to a normal Android user. On Android, rooting can also facilitate the complete removal and replacement of the device's operating system, usually with a more recent release of its current operating system.