CLEAN is an algorithm published in 1974, which cleans up images produced by radio interferometry, producing an image with less influence from the effects of the beam's side lobes and of sampling (i.e., the incomplete coverage of the baselines), an early and very well-known algorithm to accomplish this. I.e., it produces a clean image from a dirty image. It is an influential invention, widely used, and has been both a basis for modifications and improvements and a common standard by which newer techniques are judged. It essentially applies a deconvolution, if you look at the initial image as a convolution of the "true" image and the effects of the telescopes. It is designed for and best suited to point sources, which tend to "show through" the obscuration; it picks them out and de-emphasize signal unrelated to them, which is likely to be noise.
Among the subsequent variants of the CLEAN algorithm to reduce the computation include the Clark CLEAN algorithm and the Cotton-Schwab CLEAN algorithm. Some variants are also aimed at handling extended sources.