Originally, while Ingress was in beta, there was no open enrollment; you had to be invited by an existing agent. To do this, agents had to use invites which were periodically distributed by Niantic Labs. Now that the game is out of beta, getting an invite from another agent is no longer required to join.
Invitations are still useful, however: every person that becomes an Ingress agent through one of your invitations will award you 3,000 AP. Additionally, each of those that reaches level three will count towards your Recruiter medal. The number of invites you have are displayed in the tab itself and on the recruit screen.
Tap the “Recruit Agents” button to view a list of your contacts with email addresses; tap the “Invite” button for that agent to send them an email inviting them to become an Ingress agent. If you want to invite someone whose email address is not in your contacts, you can enter their address in the field at the top and tap the “Invite” button next to it.