You (and anyone else who uses your computer) are a user. By default, a user’s files are only accessible by that user. Different users have different access to files, applications, and directories (folders). A user account is the sum total of the applications and files used to create the environment a user logs into.

A username identifies your user account to yourself (and to other users). It's the name you log in with and the directory you own; /home/username. Your username is a member of certain groups. The groups to which your username belongs tells the system what permissions you have with what (kinds of) files.

User Privileges 2

Root is the system administrator. It has permissions to access all commands and files on the system. Root has the ability to modify everything in the system and control permissions for any user; including itself.

To protect the system from potentially harmful commands, the root account is locked. A user has temporary access to the root account by prepending a command that requires root priveledges with the word sudo (SuperUser). Sudo asks for the user's password before executing the command.

See the definition of root at the Linux Information Project and RootSudo on the Ubuntu Community Help Wiki.