That's pretty much right. Depth of field is how much of the picture is in focus, or the depth of the focal plane - it can be anything from a few millimeters (which is about what this was), to a meter or two, to infinity. (You can set most lenses so that everything from a certain point out to infinity will be in acceptably sharp focus; this is called the hyperfocal distance.)
When you focus a lens, you're moving the focal plane back and forth until the part of the picture you want is in focus. The depth of field is effectively controlled by two things: Aperture and magnification of the subject. Making the aperture wider makes the depth of field narrower; increasing the magnification (effectively moving the subject closer to you, either by moving yourself or using a higher zoom setting) also makes the depth of field narrower.
So to get a picture like this, with a very narrow depth of field, you want to use a wide aperture setting and a high magnification. In this case, I used a telephoto lens with a magnification about 10x a normal field of view.
One final term you'll often see used about these kind of shots is bokeh. Basically, bokeh is the quality of a blurred background; there isn't a precise definition, and it's a pretty subjective thing. In general, 'good' bokeh is smooth and doesn't distract from the subject; 'bad' bokeh calls attention to itself and away from the subject. However, some photographers deliberately try to make bokeh that calls attention to itself - rendering lights in the background as bubble-like circles, for example - as an artistic effect.
no subject
When you focus a lens, you're moving the focal plane back and forth until the part of the picture you want is in focus. The depth of field is effectively controlled by two things: Aperture and magnification of the subject. Making the aperture wider makes the depth of field narrower; increasing the magnification (effectively moving the subject closer to you, either by moving yourself or using a higher zoom setting) also makes the depth of field narrower.
So to get a picture like this, with a very narrow depth of field, you want to use a wide aperture setting and a high magnification. In this case, I used a telephoto lens with a magnification about 10x a normal field of view.
One final term you'll often see used about these kind of shots is bokeh. Basically, bokeh is the quality of a blurred background; there isn't a precise definition, and it's a pretty subjective thing. In general, 'good' bokeh is smooth and doesn't distract from the subject; 'bad' bokeh calls attention to itself and away from the subject. However, some photographers deliberately try to make bokeh that calls attention to itself - rendering lights in the background as bubble-like circles, for example - as an artistic effect.