Echochrome has a very simple design in mind, but like many great games, being simple to learn doesn't mean it's simple to master. Each level is a series of walkways and columns with various black and white holes sprinkled about. Your goal is to get the character (depicted as a drawing model or "woody" to all of the echoes (shadow versions of him standing still) positioned all over the place.
You don't control the character directly; he is little more than a lemming (except he won't just walk off the edges). As he follows the path in front of him, you can rotate the world and reshape the way it is structured based on your perspective. It sounds weird, I know, but the most basic rule is, if you don't see it, it doesn't exist.
For instance, I mentioned two types of holes, black ones and white ones. Black ones cause your character to fall through the floor, while white ones launch him into the air. If you don't want the woody to use the hole, simply rotate the world so you (the player) can't see it. Out of sight, out of mind, he just keeps on walking as if it isn't there. The same goes with gaps between platforms - if you cover it up, he will just keep on walking as if it were connected.
The other major mental bender to work out is how to use those holes. I said that walking into a black hole causes your character to fall down. It isn't like he falls down in 3D space and only the floor directly below him can save him; instead, if a panel looks like its below, then he will land on that, and the same thing goes for higher walkways when he is launched into the air.
All in all, it's a really interesting concept and I'm not sure if it can be fully comprehended in words. Much like The Matrix, I can't tell you about it, you have to see it for yourself. In order to get a better grasp on the how the game works, I would suggest finding some gameplay videos of it.
Echochrome offers three modes, Freeform, Atelier and Canvas. Freeform lets you play a random level that you have on your system. This includes both the 56 levels that come with the game and any user-created ones that are downloaded when you boot up Echochrome. Atelier lets you play any level you want (that's right, no forced level progression), which are grouped into eights. Each row (labeled by a letter) is noticeably more complex than the one above it. The last mode, Canvas, is the level editor.
The level editor is interesting, because it really forces you to think differently. Even if you've made level mods before, having to think about a world where perspective is everything means you have to really consider balance and have a lot of people play your level before you declare it done, because there seems to always be multiple ways to get to the designated echo.