Everyone will get their hands on the demo for God of War: Ascension on February 26, but some will get access to it on February 20, provided they prevail in some kind of social media sign-up challenge that's been going on for the past 10 days.
The "Rise of the Warrior social challenge," as it's called, will give a winning side ("Spartans" or "Trojans," and your membership appears to be determined randomly when you sign up) once it becomes the first to reach 10 million points in what appears to be a trivia challenge. Obviously, inviting a bunch of your friends to this helps the cause, that's why they're doing it this way.
The big reason for participating, says Sony, is "you will earn exclusive multiplayer treasures from the Gods that can only be attained from this experience," so there's that, too.
Single Player Demo Early Access Date [God of War blog]