Depth of field is the amount of distance between the nearest and farthest objects that appear in acceptably sharp focus in a photograph.
Depth of field means how much of the image is in focus. You can have a narrow depth of field, where only a small part of the image is in focus, or you can have a larger depth of field, where everything is in focus. Depth of field is controlled by the aperture. A larger aperture means a narrower depth of field.
What is 'depth of field'?
A camera can only focus its lens at a single point, but there will be an area that stretches in front of and behind this focus point that still appears sharp.
This zone is known as the depth of field. It's not a fixed distance, it changes in size and can be described as either 'shallow' (where only a narrow zone appears sharp) or deep (where more of the picture appears sharp).
Why do I need to know about it?
Because depth of field has an impact on both the aesthetic and technical quality of a picture. Sometimes you'll want to use an extensive depth of field in order to keep everything sharp.
A classic example is when you're photographing a landscape, where generally the most desirable outcome is to capture detail from the foreground to the horizon.
Other times, a shallow depth of field will be preferable. It enables you to blur background and foreground details, causing distraction to melt away and allowing you to direct viewers to the focal point in a picture.