Fire affects soil through two means: increase of temperature and removal of plant matter. The latter has the strong effect of increasing erosion. Usually, soil is covered by a litter layer of plant debris. This is often burned off by fires, causing the soil to be exposed. In addition, if plants are killed, their roots will cease to hold the soil together.
The temperature increases caused by fires can have effects on the characteristics of soil. First of all, much of the organic matter in soil will be volitalized and removed. Also, other minerals and compounds may be volitalized. In most soil there is a layer of hydrophobic soil, which prevents or inhibits water absorption into the soil. A fire may drive this layer deeper and make it larger. This has important implications once it rains, as everything above this layer is strongly subject to erosion. High temperatures of soil also may kill the biotic components of the soil, which has strong effects on the soil's properties. After a fire passes, the soil becomes exposed, and is more prone to temperature changes. In areas prone to permafrost, the soil will freeze slower, but much deeper, and stay frozen longer than unburnt soils. Counterintutively, moisture in soil actually allows it to heat up faster and deeper than dry soil, since water conducts heat well. However, the temperature can not exceed 100c for long periods of time until the water is vaporized.