The default manager role enables users assigned the role to access courses and modify them.
The Manager role is a 'real role', similar to Administrator (but much safer to use).
The way permission checks work in the Moodle code is that there is a function called has_capability. For admins, has_capability will always return true, no matter how the roles are set up.
However, the Manager role is a normal role, like Course Creator, or Teacher. By default the Manager role has almost every capability but, because it is a normal role, you can edit that role if you choose (there is no way to edit what permissions an Administrator has). Best-practice might suggest that Admins should normally use a Manager role, and not use an Administrator account.
This is similar to the way you are recommended not to log into Linux as root.
The Manager role therefore allows a site Administrator to give very powerful roles to others who are assigned a Manager role, but without having to give them a full Administrator role.
Assigning someone the role of Manager
You can give someone the manager role sitewide(to enable them for instance to add new users) by going to Settings>Site Administration>Users>Permissions>Assign system roles, selecting the Manager role and moving over your chosen user.