From Wikipedia:

Freezer burn is primarily based on the fundamental physics of sublimation. Water evaporates at all temperatures, even from what appears to be solid ice. For example, ice cubes in the freezer will shrink and eventually disappear. When the constantly oscillating moisture molecules in the meats and vegetables stored in the freezer migrate to the surface, crystals of ice outside of the solid food are formed. The parts now deprived of moisture become dry and shriveled and look burned. In meats, air can cause fats to oxidize.

This process occurs even if the package has never been opened, due to the tendency for all molecules, especially water, to escape solids via vapor pressure. Fluctuations in temperature within a freezer also contribute to the onset of freezer burn because such fluctuations set up temperature gradients within the solid food and air in the freezer, which create additional physical motivation for water molecules to move from their original positions.

It is possible to slow down freezer burn by filling plastic milk containers with water (leaving room for expansion) and keep them in the freezer to help maintain the temperature. Proper packaging can also help delay freezer burn because small, air-tight packaging allows local homeostasis of humidity, and, to a lesser degree, temperature, although most available packaging does not do this perfectly.

Meats and vegetables stored in a manual defrost freezer will last longer than those stored in automatic defrost freezers. That is because the temperature of a manual defrost freezer remains closer to 0 °F/-18 °C while the temperature of automatic defrost freezers fluctuates. Food with freezer burn, though dried and wrinkled, is safe to eat. However, food afflicted with freezer burn may have an unpleasant flavor.