Acid washing is the process of washing a car in acid. This is done to remove metal fallout or contamination from cement, concrete or limescale. The car's paintwork is coated in acid, washed, and then the acid is neutralized using a mild caustic chemical. It is left on the car long enough to break down lime or eat away metal particles but not long enough to damage your paint, which is fairly resistant to acid.
There are now products on the market which are effective against metal fallout which are less harsh, however acid washing might still be used in cases of particularly heavy contamination and for the removal of limescale or concrete contamination.