Montag is reflecting that both people and the Sun "burn", and therefore between them, everything is burned. I don't think he's just saying that things are literally burned, but that they are consumed, destroyed or otherwise used up. Montag thinks one of them (either people or the Sun) has to stop burning, and the Sun obviously won't, so it must be people. If they don't stop, nothing will be left.
The obvious answer is that they are burning books, but we can probably extend this within reason to include all forms of knowledge, as well as the nature of humanity and the world's natural resources, and human lives as well.
Montag doesn't specifically say how this is hurting their society, other than to insinuate that the Sun burns "people and Time" without any help from him, possibly suggesting that he's pushing humanity towards extinction. I think the societal threat is meant to have been seen throughout the book, and reflected upon by the reader in the same way that Montag is reflecting on it in the river; without specifically detailing it. There is clearly something missing from most of the people in the city and Montag feels as though he's been woken from a dream, so we can only assume that all this burning is stripping something essential from the humanity of this society.