sudo is 'Switch User and Do'. You can still do all of the same things that you can with su, but you can also build a ACL that specifies what users, commands, and arguments a user is allowed to invoke.
The /etc/sudoers file is described using Extended Backus-Naur Form (EBNF) rules. Most people just add their user with a glob. Something like this:
`miah ALL=(ALL:ALL) ALL`
But you can go MUCH MUCH more complex. I'm going to use some examples from the man page.