Depth of Field

Depth of field is the distance between the scene which is acceptably sharp. It also isolates the foreground from the background. The foreground stays sharp while the background is out of focus. Most of the photographers use a shallow depth of field to be creative and sometimes hide the distractions from the background. In this example you can see how I isolated the head of the cat from the background. I've used a 50mm lens with an aperture of 1.8 to produce a shallow depth of field. 

Depth of Field explained by Mark Wallace

Aperture as I've said earlier is only one of the factors that affect depth of field. Distance from the camera to subject and focal length are also factors that affect depth of field. The greater the distance from the subject the greater depth of field you'll have, the closer you are from the subject the shallower depth of field you'll have. Same with the focal length, visually the wide angle lenses make the subject farther while telephoto lenses magnify or make the subject closer.

There is also a useful tool called depth of field calculator here that might help you decide. It's only a guide and I suggest that you practice more on shooting to get a visualization on how aperture, focal length and distance from camera to subject will affect your image sharpness.