The idea behind incineration is that you have a piece of something that is capable of burning and burning it at a high enough temperature breaks all the molecules inside down into smaller pieces. Or, to put it slightly differently, if you have ever smelled burnt plastic, it smells really bad. If you burn plastic at a high enough temperature, it no longer smells bad. High temperature makes molecules break apart into smaller pieces, smaller pieces are generally better for the environment, and they usually don't smell as bad.

This sounds good, but you need a really high temperature. >1500F should do it. In my city, we incinerate some trash. People are too good at separating the trash though, so most of the stuff doesn't really burn. They need to use paper from the recycling to make sure the temperature is hot enough to actually incinerate the trash.

Now, we could let all the trash just sit there. Would this be better?

Trash that just sits there a) takes up space b) doesn't smell good and c) doesn't do anything for us.

a) is a big problem in some places in the world, but not so much in America. We're fine letting big piles of garbage sit there. Not our biggest concern.

b) is a more interesting one, garbage does not smell good. Why? It's decomposing. Decomposition puts off a lot of methane, bacteria come in and break the trash down into methane and a bunch of other molecules. Methane holds a lot more heat than Carbon Dioxide (in terms of the 'global warming potential' [1]). For every 25 tons of CO2 emitted, that is equivalent to 1 ton of methane over 100 years. Takeaway: methane is bad, CO2 is better than CH4. Also, because trash doesn't smell good you get the 'NIMBY' effect, so instead of placing the final destination of trash close to the producers, we now need to transport garbage far away so we don't see or smell it. This is bad, magic in society is almost always bad because you lose perspective on how [insert adjective] something is. I never realized how dirty the water was until I saw it, or how smelly the garbage was until I went to the dump. My garbage doesn't smell that bad, but everyone's garbage and months of decomposition will make it smell. If trash is far away, it's out of sight and out of mind, you don't realize how much of an impact people have with trash.

c) Garbage doesn't do anything for us, it's merely that - garbage. It's served it's life, it's over, it just sits now. Why not try to get something out of it? Why not kill two birds with one stone? We always need heat for something, and if we can burn trash and get heat, that would be better than burning natural gas and letting garbage rot. This idea has been applied in a number of places around the world, it's called District Heating. Hot water is routed into your house, rather than having a separate water heater (homes may still have one to heat the water up more) [2] And this also has a hidden advantage - people always make garbage, and people always need heat. The waste stream can now be a useful product in the society, and a 'closed loop' society is a little bit closer.

[1] http://en.wikipedia.org/wiki/Global-warming_potential

[2] http://en.wikipedia.org/wiki/District_heating