"root" is the name of the "super-user"--namely the user that has all powers and privileges, and who sets the privileges for all other users.
Normally, general-purpose applications are set up so that all users can run them. In many cases, the "run" (AKA "execute") privilege is assigned to a group---eg sound, video, CD, etc. In these cases, you simply need to assign user(s) to the appropriate group.
You can read up on users, groups, and permissions in many places, but I would start with http://tldp/org
I would also buy a copy of "Linux in a Nutshell" from O'Reilly