From LQWiki

A "cleanroom" is an area in manufacturing or research facilities or the like which is kept free of contamination from the outside through various measures including controlled environments and protective suits.

Drawing on this concept, a cleanroom implementation, when applied to software development, most often refers to developers attempting to clone the functionality of another piece of software without seeing the source code so as to be sure that their "environment" is clean and no "contamination" from the other product occurs.