Normal users pretty much are limited to their home directory located at /home/$USER or ~/. They are generally free to view files located on the filesystem however.
Admin accounts have more permissions and likely can modify system files. This doesn't mean a admin has access to everything, they may only have access to files located in /etc/ for example. They may have access to sudo which is a selective way of permitting high level actions.
Because of this, what defines a "admin" can be blurred.
In most single person systems (home computer) admin can be equated with root access.
Root is the highest level. root can do anything it wants, whenever it wants. So be careful in root.