Dry ice is a solid form of CO2 gas and from the moment it is produced it will always try to get back to being a gas. This change of physical state is called sublimation. Accelerating dry ice particles to a high speed using compressed air and impacting them onto a solid dirty surface will drastically increase the sublimation process and generate large volumes of CO2 gas within the dirt layer.
The gas generation within a restricted space will break up the dirt layer which will then be blown away by the compressed air. In conventional abrasive blasting the process appears similar, but as dry particles are very soft they do not clean by abrasion so the substrate remains physically unchanged. This can be proved by cleaning a polished moulding tool with dry ice. There will be no change to the mirror finish on the tool.