Skip-bleach Processing refers to a technique whereby artistic ends are achieved through a kind of “incorrect” processing of colour film. In all film stocks, it’s silver that reacts to light. In colour film stocks, when the silver reacts to light, it causes a colour dye coupler to form colour dye next to it. In developing, the silver itself (which is black after exposure and developing) is washed – or “bleached” – out. If you leave the silver in the print “skipping” or “bypassing” the bleach step – the image will have black silver sort of contaminating all the colours. The contrast increases, the blacks get very dense, and the colours get darker and more de-saturated.
Spielberg’s Saving Private Ryan made use of a variation of skip-beach processing called ENR, created by Technicolor Labs. In this case they run the print through a second black & white developer to develop in the silver permanently (with a skip-bleach print, you could, in theory, later still wash out the silver.) By varying the strength of the developer, they can control how much silver gets left in – while the skip-bleach process leaves ALL the silver in. So the ENR process can be as subtle or as strong as you like. For example, the prints for Evita used a 30% ENR, the prints for The Game used a 60% ENR, and I think that Saving Private Ryan used a 90% ENR. Deluxe Labs also has a ENR process now called ACE. Their skip-bleach process is called CCE.
This answer is based on a response by David Mullen to a similar question on RAMP.