Washing a deck of cards is more than just another term for cleaning a deck of cards. Washing, also called scrambling, is a simple, but effective, method of quickly randomizing a deck of cards, especially one that has recently been verified.
To wash a deck of cards, just spread it face down on the table in two rows. Then, use your hands to slide the cards around the table in a circular motion. Periodically, change your motion in a random fashion, moving the cards clockwise, counterclockwise, away from you, toward you, etc. After a few minutes of this, gather the cards back up into a stack and square it up. The deck can now be shuffled in a normal fashion.
While this might seem like an amateurish way of shuffling cards, it randomizes the cards much more quickly than traditional riffle shuffles. Casino dealers wash decks of new cards immediately after verifying them whenever deck changes occur and new games are opened.