When you look at photographs try to check out the background as well. How a lens renders the out-of-focus background is called the bokeh. It's the quality of the out of focus part. But, like any qualitative measurement, there are many factors involved (some real, some imagined) and a lens with great bokeh can still end up making some funky backgrounds.

Typically this lens does a great job with bokeh. Yet even with a shallow DOF on this shot I think the brightly lit background, while diffused, ended up with enough variations to be distracting.

To get an out of focus background you need a shallow depth of focus (DOF). This is typically accomplished by opening the lens aperture wider and increasing focal length. Aperture is the size of the hole letting light in. If you see something like f/2.8 that's a pretty wide open aperture, while f/22 is a pretty small opening. f/2.8 lets in more light and the camera shutter needs to be "open" a shorter time for proper exposure. While f/22, with its small opening, requires significantly more time to get enough light for a good exposure. The type of photo you are taking determines which is more suitable and the camera/lens/lighting determines which are possible.

For the photo above I was around 20 feet away, a 280mm lens focal length, and f5.6 aperture. According to this calculator there was around 4.3 inches DOF. To get the same DOF with my old point and shoot Nikon 775 it would have to be cranked to its longest focal length, 17.5mm, opened up to f/2.8, and I would have had to figure out a way to get within 20 inches of the chickadee.

Other resources: maximizing focus, the mathematics of DOF, and wide angle lens DOF.