This is what a typical coal forest would have looked like – warm, humid and swampy. However, it is important to keep in mind that this was not so everywhere on the globe.
This type of biome was present in tropical areas, but further out were temperate forests. However, due to swampy areas having a much higher preservation potential (the mud pits are anoxic!), much more is known about them.
In the Carboniferous, we have the very sudden appearance of a high diversity of flying insects. In fact, many of the insect orders known today were already living in the Carboniferous forests, as well as many now-extinct orders.
This is apparently an explosive radiation, but it may be another case of a Romer’s gap, as we don’t really have any transitional fossils showing the stem-groups of these very diverse insect orders. Unlike the Cambrian Radiation, where the stem-group fossils are there, here we really are dealing with a gappy fossil record and only an apparent burst of diversity, not a real one – although this conclusion can be disputed as well!
In this diagram, the still-living orders that originated in the Carboniferous are: the mayflies (Ephemeroptera), dragon- and damselflies (Odonata), grasshoppers, crickets and their ilk (Orthoptera) …
Diagrams source: Labandeira, C. C. & Eble, G. J. 2005. The fossil record of insect diversity and disparity. In: Anderson, J., Thackeray, F., van Wyk, B. & de Wit, M. (Eds.). Gondwana Alive: Biodiversity and the Evolving Biosphere. Witwatersrand University Press.