The depth
of field corresponds to the area (depth) in a picture
which appears to be in focus. There is an area in front of and an area
behind
the subject you are photographing which can be in focus. The depth is
being
influenced by different factors related to optics. The aperture is one
of the
major factors influencing the DOF. The bigger the aperture (small
f-number) the
smaller the DOF. Having a big aperture (f1.4 or f1.8 or even f2.8
lenses) allows
to nicely blur the background of a picture because the DOF will be
relatively
thin. Using a long focal distance is also reducing the DOF. If you
shoot with a
wide angle, even fully open, you will have quite some DOF, while using
a long
telelens (say 400mm) even if you close down the diaphragm, you'll have
a
relatively thin DOF. The DOF expressed as a distance is also depending
on the
distance to the subject.
The DOF is also being influenced by the size of the film/sensor and its
resolution.
To calculate the DOF for a specific sensor, lens and aperture combination, there are several tools available on the net. My favorite tool is http://www.dofmaster.com
Typically the way a photographer can control DOF is by selecting the focus point and to play with the aperture (low f-number - thin dof - high f-number - large dof). The other parameters are fixed (focal length and sensor characteristics).
An example of a picture with superthin DOF (105mm f1.8 lens @1.8 on a D200)