After compost cools down it is still pretty rough. Micro and macro-arthropods are vital in this phase. They do the shredding work. Then you have the organisms that break down their excretions and so on. Compost particles get smaller and smaller the longer it sits.
Fungi are at work during the curing phase as well.
When red worms leave your compost it is in pretty good shape but let it sit another year if you want to run your hands through some really nice material. You can feel the energy in it. The particle size by this time is very small. The smell is rich, sweet and very earthy. Smell the difference sometime between compost like this and poor soil.