So what exactly is heavy rain?

Don't know much about the game, but wikipedia says it may be subtitled "The Origami Killer"

From what I can tell, Heavy Rain will be a lot like another game for the PS2, PC and Xbox called Indigo Prophecy in the states, and Farenheit in other countries. It's basically an adventure games. You take control of a character at a certain point in his life. You can basically walk around and interact with objects around you as you would do in real life. There are many ways to interact including having conversations in which you may be given 4 or 5 different choices of what to say and must decide which to say in a given amount of time. What you say can impact what happens in the game. In Indigo Prophecy, you also had a stress meeter. It had different conditions such as Neutral, and Depressed, all the way to Suicidal.

It's extremly hard to describe this kind of game, but let me tell you, it's an f'n amazing and unique experience. Watch a video of the first part of Indigo Prophecy on youtube. Or better yet, play the game yourself and you'll realize why people are going nuts over this game.