The center of the North Pacific Gyre is a relatively stationary region of the Pacific Ocean (the area it occupies is often referred to as the horse latitudes). The circular rotation around it draws waste material in and has led to the accumulation of flotsam and other debris. While historically this debris has biodegraded, the gyre is now accumulating vast quantities of plastic and marine debris. Rather than biodegrading, plastic photodegrades, disintegrating in the ocean into smaller and smaller pieces. These pieces, still polymers, eventually become individual molecules, which are still not easily digested. Some plastics photodegrade into other pollutants.
North Pacific Gyre (Click here to see an animated map)
The gyre is discussed in Alan Weisman's The World Without Us as an example of the near-indestructibility of discarded plastic.