When you first start taking pictures you concentrate on the subject, making sure it's well-focused, positioned appropriately in the frame, well-lit and so on. But soon you realize, as we all do, that concentrating on the subject isn't enough. Frequently we learn this when some element of a background—a palm tree, maybe, or a telephone pole—appears to grow strangely out of a subject's head. This is, generally speaking, not good. So, we learn to start paying attention to the background. And the main thing we work on is simplifying it.
A busy background competes for attention, drawing viewers' eyes away from the subject. So, photographers learn—some more quickly than others—to simplify the background. Frequently this is done by recomposing a scene, repositioning the camera so that what was an offending background is now a nice, clean backdrop on which to photograph the subject. But, there can be an even better, even simpler way to assure that your backgrounds are cleaner and simpler than ever: to ensure that they're well out of focus.
Making backgrounds out of focus is simple enough. You just start with a wide-open aperture—say f/2 or f/2.8, for instance—and you'll find that the background is much less sharp than it would be at f/8, f/16 or, heaven forbid, f/32. For a simple background, starting with a wide aperture is a recipe for success. But, it's still not a guarantee. For that, you need to change lenses.
The combination of a telephoto lens and a wide-open aperture will create compressed backgrounds that are out of focus due to super-shallow depth of field. This is a great way to eliminate any distraction from behind the subject. But, isn't there a problem? Isn't a 70mm lens going to look dramatically different than a 24mm lens? Obviously, yes. But, when you move your feet, you can keep the subject size the same. Up close, with a 24mm lens, you can fill the frame with a subject's face, just as you can from farther away with that 70mm lens. The relative sizes might be the same, but the backgrounds will be dramatically different. So, whenever possible, use a nice long lens and a wide aperture to minimize depth of field and simplify the background. It's a simple technique, but the effect is quite powerful.