One of the more effective tools to take advantage of in photography is an effective use of depth of field. Depth of field refers to the sharpness of an image, from foreground to background. When we refer to a shallow depth of field, we mean an image that is sharp in one section and blurry in others. On the other end of the spectrum, a deep depth of field is one in which the entire image is sharp and in focus.
Achieving a shallow or deep depth is done by adjusting the size of your camera's aperture, the hole that determines how much light reaches your camera's film or image sensor. A larger aperture setting allows more light and a smaller setting less. We measure the aperture size in f-stops (the f stands for focal length), and, in a somewhat counter-intuitive fashion, the smaller the f-number, the larger the aperture. So, an f/1.8 will be a larger opening, and an f/22 will be a very small opening.*
If used effectively a shallow depth of field does a great job of highlighting the subject and creating an almost dreamy quality to the photo. It is especially great for outdoor portraits. On the other side of things, a deep depth of field allows you to capture the entire gist of a photo. I've found this especially useful when the background is as important as the main subject.
Below is a study of my grandfather's old Polaroid camera (and trying out my homemade light box). I focused on the ring of the lens, and the images progress you'll notice the detail getting sharper throughout the image. If you look at the dial on the left, blurry in the first picture, you'll gradually make out the number "4" as the depth of field becomes deeper.
Like any photography technique, my best advice is to experiment as much as possible. You'll find that the more you work with your stops and seeing the different results, the better you'll be able to hone in on the style that best fits your needs.
*This is also why lenses with a low f-number are much better for shooting in low-light situations as they are allowing in a lot more available light.