Depth of Field (dof) refers to what around the subject ( Focal Point ) is or is NOT also in acceptable focus... (ie. what is clearly visible).
<<< In the samples to the left.
The corner of the building is the Focal Point or subject the camera has focused on.
The top image depicts a shallow narrow or short Depth of Field. One in which the subject is in focus but little else is. This technique is used to drive the viewers eyes to the point of clearity as it is disconserting to look into and at blurry elements.
The bottom image depicts a great or long Depth of Field. One in which everything appears to be in focus. This technique is used to allow the viewer to explore the image as a whole and develop a narative or story that the image is trying to convey.
Below shows the relationship between the aperature setting and the depth of field that may be produced using those settings.