Depth of field is the zone in front of and behind your focus point that still reads as acceptably sharp, controlled mainly by aperture, focal length and focus distance.
Depth of field is the main tool a photographer has for pointing the viewer's eye. A shallow zone, roughly what you get from f/1.4 to f/2.8 on a fast prime, lifts a face off a cluttered street so cleanly that there is nowhere else to look. A deep zone keeps a rock two feet from the lens and a ridge a mile away both readable in one frame. Getting it wrong is not a small error.
Shoot a five-person group at f/2 and focus on the front row, and the back row lands soft enough that people notice their own faces are blurred. Shoot a wide landscape at f/2.8 to keep the shutter fast enough to hand-hold, and the mountains you drove three hours for turn to mush. Depth of field also changes with focal length and focus distance, so the same f-number behaves very differently on a 24mm lens up close than on a 135mm across a field.
Put a 50mm lens on a full-frame body and focus on someone standing 3 metres away. At f/1.8 the sharp zone runs from about 2.8 to 3.2 metres, a little over 30 centimetres, barely enough for a face turned slightly off-axis. Stop down to f/8 and it grows to roughly 2.4 to 4.1 metres, so a second person half a step back stays sharp. At f/16 it stretches from about 1.9 metres to well past 6.
Focus distance pulls just as hard as the f-number. Move back to 10 metres at f/1.8 and the same lens now holds more than 4 metres of sharpness, because the zone expands quickly as the subject gets farther from the lens. That is why a tight headshot and a full-length portrait taken at one aperture do not behave the same way, and why focus-and-recompose is riskier up close.
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