Bokeh (pronounced bow-kuh): Japanese for really cool out of focus backgrounds in photos!

The background of a photo is out of focus because of the aperture chosen. A large aperture will cause most of the background to be out of focus. This is true for every lens, but some lenses give the out of focus background a special character–bokeh. No one talks about the bokeh of a 50f1.8 lens other than to say it’s crap. You will hear people talk about the bokeh of a 200f2, or one of the most famous Canon lenses, the 85f1.2LII, which was used to make the sample photo above.
Don’t expect to see much out-of-focus background when using a small sensor camera, such as a cell phone or a point-and-shoot. The physics/optics of these cameras mean that almost everything is in focus, much as in a pin-hole camera photo. (As an aside, there is much irony in the use of f64 with a large view camera of the kind used by Ansel Adams–although the format lends itself to producing massive bokeh, the members of the f64 club used incredibly small apertures in order to increase the depth of field when making landscape images.)
Bokeh is not something you have much control over, other than buying a lens with good bokeh. It’s also not something to get worried about. Most people who view your photos are not going to get all critical about the average bokeh your lens displays!