When I usually place a picture in the background on my computer I either use one image that gets mirrored on both monitors or use one large picture and span it across both monitors. But I discovered you can put a different picture on each monitor of your dual monitor setup.
Right-click on your desktop and click on Personalize. In the window you'll notice a Browse button just under 5 picture thumbnails. You can add picture (or just use what's there) to replace the five seen by using the Browse button and selecting a picture on your hard drive.
It will occupy the first thumbnail slot, and the rest get bumped one space to the right with the last one being eliminated form the group.
So pick your first picture. It will first display on both monitors. Now for the second picture that you want on a second monitor, right-click on the picture and you'll get a little pop-up menu. Pick your monitor.
If you don't know which monitor is number one or two, just right click on your desktop, click on Display settings. In the window that opens, click on the Identify button. A number should pop up on each monitor.
This should work even if you have more than two, just adjust accordingly.