The term implies that the design team works in an environment that is 'clean', or demonstrably uncontaminated by any knowledge of the proprietary techniques used by the competitor.
Typically, a clean room design is done by having someone look at the system to be reimplemented and having this person write a specification. This specification is then reviewed by a lawyer to ensure that no copyrighted material is included. The specification is then implemented by a team with no connection to the original examiners.
A famous example is from Compaq who built the first clone of an IBM computer through a clean room implementation of the BIOS.