Depth of field is the distance between the nearest and the furthest objects giving a focused image, or, the zone of acceptable sharpness within a photo that will appear in focus. Large aperture = Small f-number = Shallow (small) depth of field. Small aperture = Larger f-number = Deeper (larger) depth of field.
Shallow Depth of Field
A shallow depth of field is when a part of a photograph is isolated and in focus while the background and other objects in the photo are blurred and out of focus.
Deep Depth of Field
A deep depth of field is used mostly in landscape photography. It helps to get as much of your scene in focus as possible.