Depth of field (aka DOF) is a technical term referring to how much of the picture is in focus. A large depth of field has lots in focus, while a shallow depth of field only has the main subject in focus.
The depth of field is controlled by the lens aperture, described by its f-number. Smaller f-numbers (f/1.8 for example) mean shallower depths of field; larger f-numbers (f/8 for example) mean larger depths of field.
So now, lets see how it works:
This portrait was shot @ f/2.0 with Canon EF 50mm f/1.8 Mk I. As you can see main subject is perfectly in focus, while the background is blurred. (shallow depth of field)
Mastering DOF is very important for a starting photographer, it allows greater control over the final outcome, and considerably increases creative scope. So put your camera in AV (aperture priority) mode and experiment with different numbers.