Subscribing to a user's profile allows you to keep up to date on another user's submissions. By default, you will recieve a PM anytime this user uploads a new media item. Optionally, you can recieve e-mails as well.
Subscribing to a profile will add a "Subscriptions" box to your profile page. From there, you can edit the options for each subscription, choosing between PM or E-mail or both as well as removing subscriptions.