So the basic idea is that the world is freezing and you have to burn stuff to stay alive. Burning things nets you money to buy more things. Burning something that cost you 5 coins nets you 6 coins (or more depending on if you combo it with something else).
Of course it gets a lot more darker than that, these are the same people who made World of Goo after all. See, the things you're burning are alive and act accordingly to being burned. There is this deep mystery about everything and it's all very cryptic and dark. They add lots of humor (also dark) with flavor text and the way things burn. The graphics are really clean and simple but realistic in a lot of ways as well. The fire and physics of everything add another layer to making you feel queasy about torching that stuffed animal or box of chocolates.
The real replay value comes from combo burning items. They give you a list of names like "LOL KITTY" or "SPRING TIME" and it lists the number of items that make up a combo. You have to then figure out what those objects are by burning things relative to the name together. For example "SPRING TIME" was a packet of sunflower seeds and a clock. Obviously as you unlock farther into the game the combos become longer, requiring 4-5 items at once out of all the various catalogs. It adds a challenge and the need to think in an otherwise odd, mysterious little game.
The story so far is haunting and disturbing yet enigmatic enough to keep going to figure out what the hell is going on. So besides the brain teasers and wicked story, this game is a pyro's dream. It's utterly cathartic to just burn stuff if you can make it past the screaming and burning looks of agony.