According to the official PlayStation blog, "Four Days" is a "live online mystery that plays out in real time across three weeks." Daily tasks for players to complete will be available Tuesday through Friday for each week the webgame is live.
To check it out, simply register at the Heavy Rain website and you'll receive an email shortly thereafter with your first set of instructions.
Players will receive an email at the beginning of each of the three weekly events that contains instructions on what to do next. The post also mentions "cool exclusive content" players can get for playing. For example, people in the blog's comment section indicate that there's a Heavy Rain shirt for PlayStation Home to be unlocked.
Heavy Rain is exclusive to the PlayStation 3, and comes out in North America on February 23rd. The European mainland gets the game on February 24th, with the UK and Ireland launch following on the 26th.