At Admin Panel -> Settings -> Switches you have a switch labeled 'invitations'. Turning this on will allow your members to use a simple form on their member home main page to invite people they know to regsiter at your site.

Once you turn on the switch, an option appears under Admin Panel -> Members -> Member Settings to make registration be by invitation only if you wish (you can also just use invites without requiring them to register).

At Admin Panel -> Members -> Manage Usergroups you can set who can send how many invites. If you happen to want to let people register in multiple usergroups, depending on the group the inviter is in, you can do that as well by checking the "allow usergroup specification" box.

A major purpose of the invitations system is to allow you to do Google-style marketing. Take a product and make it available by invitation only. This makes it exclusive, and hence popular -- you get people using the site because they feel special.

Handy tip: Invitations bypass restrictions like IP bans and anti-proxy rules, so sending someone an invite is a good quick way to help them register if they report that they've been blocked in some way.