The CLEAN algorithm (Högbom 1974) (A&AS 15, 417) represents the image as a number of point sources in an otherwise empty field of view. A simple iterative procedure is used to find the locations and strengths of these point sources.
The Högbom CLEAN algorithm looks for the brightest (in an absolute sense) pixel (called a CLEAN component) in a specified region in the image (called the CLEAN window which must include all the real emission in the image). For Stokes I images (but not Q, U or V), ideally only positive components would be encountered. However noise, errors in previous CLEAN iterations and calibration errors will mean that eventually negative components will also be found. Often it is quite valid to CLEAN these negative components. Having found this peak pixel, it subtracts a fraction (called the loop gain, and generally about 0.1 or less) of the dirty beam from the dirty image at the location of that brightest pixel. This subtracted image is called the residual image. The search and subtraction loop is repeated until the sidelobes in the image are reduced to below the noise level. It is easy to see how CLEAN works if you just think about a single point source. For extended sources, one thinks of the emission as a collection of point sources. Except for point sources, the flux density units of the dirty image are not very useful. However, convolved CLEAN components do have meaningful units of Jy per CLEAN beam area, which can be converted to Jy per unit area, because the equivalent area of the CLEAN beam can be calculated.