Releasing carbon is an externality that isn't taken into account because it doesn't immediately hurt you (in your wallet or otherwise). Taxing it is simply taking that externality and putting a price on it.

Once you tax it markets will immediately respond by finding efficient, low carbon footprint alternatives to everything. That is, if people can get into their heads that capitalism is a system (to be tweaked for the benefit of everyone), not a religion.

By the way rich people will be the least affected global warming.