When you sign up for Facebook with your e-mail address and password, you're creating a Facebook profile. A profile is for non-commercial use and represents an individual. You can now "follow" Facebook profiles to see updates from people you're interested in but don't want to be friends with. This means that you will see their updates (photos, statuses, etc.) in your news feed but they will not appear on your friends list unless you add them.
A page looks similar to a profile but doesn't give you the option to add the page to your friends list. You merely "like" the page and similar to following a profile, will then receive updates to your feed. They are managed by one or several profiles. Pages give unique options to businesses that a profile doesn't offer.