Depth of Field (DOF) is how much of your image is in focus (this means how much in front and how much behind the point you focus on).
As a general rule, when taking portraits use the largest aperture your lens has to restrict the depth of field.
When taking landscapes or scenery use your smallest aperture to increase your DOF to get as much as possible in focus.
Aperture is represented by an F number on your lens, and the smaller the number (eg F4) the wider the aperture and the smaller the depth of field.
The portrait picture above has a very shallow DOF and the brook has a large DOF.
Find out more about Beck Photographichere.