Lyophilization (the technical term for freeze-drying) involves cooling down something to the freezing point of water, then dropping the air pressure around it to make the boiling point match the freezing point (lowering air pressure lowers the boiling point of water). when this happens, the solid water sublimates or turns directly into a glass without becoming liquid first.
Freeze drying is quite a bit quicker and more thorough than simply waiting for water to evaporate. It also tends to preserve the shape of the drying thing and prevents chemical reactions with the air (that do things like discolor fruit), or the growth of microbes (which are dried out and destroyed by the process).
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