When you set the focus on a lens you are picking the mathematical distance to the subject that will be perfectly in focus. Depth of Field is the area in front of and behind that mathematical point that also looks in focus.
Depth of Field can be shallow (only the exact subject is in focus) or deep (everything from right in front of the camera to the distant mountains is in focus.) Hollywood movies use this effect as part of the storytelling device. Wide shots have deep depth of field. Close-ups have shallow depth of field with beautifully blurred backgrounds, allowing us to focus on the characters emotions.
Depth of Field is controlled by two main factors:
The first is zoom. A wide angle lens produces deep depth of field while a telephoto lens has shallow depth of field. To get out of focus backgrounds in a coseup, use a long focal length lens (or zoom far in with a zoom lens). This often requires moving your camera father back to still maintain correct framing.
The second is aperture. A wide-open lens (small f-number) produces shallow depth of field while a closed-down lens (large f-number) produces deep depth of field. To get out of focus backgrounds in a closeup, open the lens aperture wide and adjust lighting appropriately. Indoors this will mean adjusting the intensity of lighting. Outdoors often requires extra ND (Neutral Density) filters to be placed on the lens to reduce the brightness of sunlight.