In the picture above, my subject was the seeds and how they interconnected with each other making long chains. Because I was using a macro lens with excellent bokeh, I was able to use some of the same seed branches as the background. The further away that the seeds were from my focal plane (the relative distance to the camera from where I focused), the more fuzzy they got. Eventually, they fuzzed out so much that they became a just a color and part of the background. I didn't need a backdrop of any kind, just a really tight depth of field and putting the colors that I wanted in the background.
A simple explanation of how to control your depth of field. DOF is computed by the focal length the lens is at, the distance you are from your focal point, and how large the aperture is (ie. the smaller the number, the less DOF). Generally speaking, the longer your focal length, the less DOF you have. The farther your focal point is, the larger your DOF. The larger your aperture, the smaller your DOF. In more layman's terms, wide angle lenses have a greater depth of field because you are generally wanting everything in focus with your wide angle view. For telephoto lenses, you can get pretty good blur except that the distances you are usually focusing on are much farther. But it is really the macro lenses where this is the most useful. A combination of larger focal lengths and very close focusing distances and a very large aperture gives you a very tight DOF. Combined with the way that the manufacturer generally builds these lenses, you get really nice circular bokeh.