Coalification is the process of converting living biomass into coal. The generally accepted sequence for coalification is shown at the left The first three elements of the process are known as the diagensis phase; the last part is the catagenesis phase. Peat is the precursor of coal, and is what is formed in the first phases.

The coalification process is roughly comparable to baking a cake, but on a grand physical scale and time scale. The ingredients are first mixed and the action of microorganisms (yeast in the case of
a cake, bacteria and fungi in peat) begin to transform the dough. 
Baking kills the yeast and chemically alters the dough from a moist, plastic material into a rigid solid. In coalification, peat is degraded by both microorganisms and chemical reactions, such as oxidation.
In the process, cellulose is substantially lost and the lignin chemical components are transformed. (Cellulose and lignin are the major structural biopolymers in plants.) Oxygen content of the peat decreases, which increases the carbon content. Water content also decreases. The ratio of aromatic carbons (graphite or charcoal-like
character) to aliphatic carbons (oil-like carbons) also begins to increase. 

As the peat is buried deeper and deeper, the temperature gradually rises. There is no oxygen input now and all biological activity has stopped. Oxygen continues to be lost and aromatic carbon increases even more. There are all sorts of other reactions that the organic material is undergoing. The details are still not clear. Condensation
reactions, as well as depolymerizations, are occurring. By the way, the temperature is not very hot. It probably doesn't get any higher than 150 C. But it cooks for millions of years. Then the land begins rising, erosion removes the upper layers. Man comes along and finds that nature has just baked a coal and taken it out of the oven.

Information provided by: http://chemistry.anl.gov