What is DOF?
Well, it stands for Depth of Field and it's controlled primarily by the aperture setting in your lens. It is the amount of in-focus bits of an image shown in the image below by the in-focus subject but a very blurry background and foreground.
If the aperture is wide open you get a shallow depth of field, if your aperture is closed you get a wide depth of field.
If you use Auto mode, the camera will do this for you to some degree, but if you want to control this and get really great blurry (Bokeh) backgrounds, then you need to learn how to use either Aperture Priority mode or go manual.
So the tip is for auto mode, get close to your subject so that the in-focus portion is a small part of the image and then your background will blur out.
Whenever you are taking photos of kids or animals put your camera on 'burst' mode (continuous shooting) so that you take multiple shots of the same scene.
Usually marked on the camera by this symbol
This will help you capture those fantastic little facial expressions that only kids and animals can provide.