Depth of field (or DOF) is, as stated above, a measure of how much of your picture will be in focus.
No lens will have everything in focus, from a section of chain-link fence touching the lens right out to infinity. when you focus on an object, say 10 feet away, you may have, for example, everything between 8 and 15 feet away in focus, but the horizon and stuff in the forground less than 8 feet away is blurry. In this case, you depth of focus is 8 to 15 feet. Most old SLRs and some new ones have a function which will actually let you "preview" the depth of field.
Depth of field depends on 2 things: 1) the design of the lens, and 2) the aperture that you use. (Shutter speed has in itself no relation at all to depth of field.) The first one, you can't do anything about (other than buy another lens). But the second you have control over. The larger the aperture (which is equal to low f/stop numbers, like f/2.8), the smaller the depth of field will be. Portrait photographers often use lenses with very wide apertures, as it allows them to have the subject in focus, and all the backgroud be totally blurred, which prevents background feature from distracting attention from the subject.
A small aperture (equal to a high f/stop number like f/16) will give you a much larger depth of field.
If you focused on a specific object at 10 feet away, at f/2.8 your depth of field may be in the range of 9 feet (inner-limit DOF) to 12 feet (outer limit DOF). At f/22, your depth of field maybe from 2 feet to 60 feet.
Note when you look at the focusing distances on your lens (any lens) are not linear, but logorithmic. This results in that as your depth of field changes by changing the focusing point (keeping the f/stop constant) the distance in absolute terms of your outer limit DOF changes faster than your inner-limit DOF. Theoretically, the inner and outer limit DOF will intersect right in front of the lens, 0 inches away.
One concept that very few people use because of the popularity of rotating ring-type zoom lenses is hyperfocal distance, which is immensely useful, as it eliminates any calculation or trial and error needed to get the correct depth of field. Tell me if you want a description of that. But you won't be using that if you use most zoom or AF lenses.
The only thing you should feel when shooting a terrorist: Recoil.