wheel is a holdover from UNIX in the dim and distant past. I'm not sure why it was named wheel.
A user does NOT have to be a member of wheel to use sudo. Who can and cannot use sudo and what privileges they have is determined by the /etc/sudoers file.
The purpose of wheel is to create a group of users who have some system administration privileges, in other words some subset of root privileges not allowed for ordinary users. sudo is one possible tool (and perhaps the best tool) for parsing out those privileges.
A default /etc/sudoers file has a commented out line that looks like:
#%wheel ALL=(ALL) ALLIf you remove the # at the beginning of the line it becomes active. At that point any member of wheel has full root privileges if they use sudo. If you want to try this please remember that /etc/sudoers must be edited as root with the visudo commandy ONLY. visudo parses the file for correct syntax. If you use another editor you can seriously break sudo.
Ubuntu does something different which, from my security professional paranoid perspective, is a really bad idea. It assigns the first standard user created sudo ALL privileges with the NOPASSWD option enabled. That bypasses wheel and effectively gives that user root privileges using sudo without ever having to enter a password. It's all very Windows-like and makes Ubuntu seem easier to use but it also leaves the door open for an unsophisticated user who knows just enough to be dangerous to do all sorts of nasty things to their system with little or no forethought.
Anyway, sudo is an incredibly powerful tool. I even use it on my own personal systems because it logs the commands I enter prefixed by sudo. If I do something stupid at least I can go back to my logs and see what I did and fix it
Learning how sudo works is a very, very good idea. Putting yourself in the wheel group is an easy way to give yourself root privileges without having to use the actual root password and with the ability to log what you're doing.
