[strike]Your monitor has 6-bit color depth per color. The more expensive monitors are 8-bit or 6-bit with dithering specifically to avoid the problem you're encountering. Check your monitor's settings to see if there's a way to turn dithering on.
If your monitor can't dither, you're going to have to either live with it, or figure out way to switch your desktop to 16-bit color (5-bits red, 5-bits blue, 6-bits green. I'm not even sure you can still do that anymore in Win 7/8 - pretty much everything is 24- or 32-bit color nowadays). If you put your desktop in 16-bit color mode, Windows will dither the 24-bit background image and it should look a lot better on your monitor.
Another option is to dither the picture to 6 bits per color in Photoshop, then save it as a BMP (not a JPG, which is lossy and will reintroduce 8-bit color). But really, there should be an option buried somewhere in your monitor's settings to dither. I don't think I've ever heard of a LCD monitor which can't do it.
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Edit: Oh wait, I just realized your screen cap also shows the problem. So the problem is not your monitor. It's either your graphics settings or the picture you've downloaded. Make sure your graphics settings are 24-bit or 32-bit color. If they are, then whoever made the image likely screwed up and downgraded the bitdepth (really easy to do if you're playing with levels on a source image with 8 bits per color). You'll need to load the pic in Photoshop and dither the background. Save it as a new pic, and use that for your background.
http://www.iceflowstudios.com/2013/tips/smooth-gradients-in-photoshop-dithering/