In your admin panel you have a switch labeled 'invitations'. Turning this on will allow your members to use a simple form in their member home area to invite people they know to regsiter at your site.

Once you turn on the switch, an option appears under settings->users to make registration be by invitation only if you wish (you can also just use invites without requiring them to register). Then in the usergroup permissions you 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.

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.