Isn't the wheel group the group that has the ability to su to root?

Is there anything else significant about this group? Any other system groups?

In the BSD world, members of the wheel group are the only users allowed to su to root. This restriction is not honored in the Linux world. Meaning, all users can su to root as long as they know the password.

The importance of the wheel group usually lies in applications or file ownership which give access permissions to the users who are in the group. For example a file could be setuid (run as root) and have execute permissions turned on for the wheel group but off for everyone else. This means the program would run as root but could only be run by root or the members of the wheel group.

Or maybe there is a file which is owned by this group so member of it can make configuration changes without needing to be root.

You get the basic idea. You might get an idea by looking at which files have a group of wheel... and permissions which are odd (+w or +x if not a directory).