The name is a lie. Dry cleaning is not actually dry.
All it means is that the liquid used to clean the clothes does not have water in it. Instead it is usually a solvent called perc. Just like the soap used at home it dissolves stains while not harming the fabric.
A [dry cleaning machine](https://en.wikipedia.org/wiki/Dry_cleaning#/media/File:Drycleanmachine.JPG) is not all that different from a home washing machine and works basically the same way.
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