The depth-of-field is the perception of distance in space in an image. It is the distance in front and behind the object of focus. Focus falls off gradually both in front and behind the object. When a point of light is in focus, is is recorded as a defined point on the light sensor of the camera or on film.
All points in front of or behind this focal point have borders which are less-than-defined. This is called the "circle of confusion," and the effect is that of a blurred edge.
The degree to which this is perceived is controlled in part by the aperture, the distance to the object, and focal length lens.
Aperture's Effect on Depth-of-field
Because the aperture is more than just a hole that lets light enter the lens, but also a means of controling how sharp the points of light passing through the lens can be, we can use this device to control depth-of-field.
A smaller aperture (a high setting, ie. f/11, f/16, f/22) produces smaller points of light on the film or light sensors of the camera. The perception is sharpness of even the points we are not focusing on.

Example of a Depth of Field. Aperture: f5.6 - Note the blurred background and in-focus subject.
Photos by Lee Gonzalez for use on WindowsPhotoStory.com only

Example of a Depth of Field. Aperture: f19 - Note that the background appears in-focus along with the subject.
Photos by Lee Gonzalez for use on WindowsPhotoStory.com only
Focal Length of the Lens
Depth-of-Field is inversely related to the length of the lens you are using. The shorter the focal length lens (wideangle) you are using, the larger the depth-of-field.
Distance to Your Subject
The distance to your subject affects the proportional distance to objects in front of and behind the plane of focus, making the out-of-focus objects more or less obvious, depending on that distance.
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