Wide color gamut, or WCG, is often lumped in with HDR. While they're often found together, they're not intrinsically linked. Where HDR is an increase in the dynamic range of the picture (with brighter highlights in particular), WCG is an increase in color: "Redder" reds, "greener" greens, "bluer" blues and more. Both provide more of an impact on-screen than the resolution increase from high-def to 4K, but in different ways.
HD TV = 16.7 million colors (256 green x 256 blue x 256 red). Even with that many potential colors, you still have the possibility of banding (which is exactly what it sounds like: bands instead of smooth transitions of colors), and you can miss out on in-between shades.
4K TV w/ WCG = 1.7 billion colors (1,024 green x 1,024 blue x 1,024 red). That means many more steps or "shades of gray" and access to over a billion colors.