The Rest of the Frame
Too often it seems as if the frame is merely an irrelevant rectangular shape surrounding the subject of an image. But the camera sees more than just the subject so why not use the rest of the frame?
The tendency for beginning photographers is to bulls-eye their intended subject, smack dab in the middle of the viewfinder, and then press the shutter release button. The thinking behind this approach seems to come down to ensuring that nothing important gets cut off if their aim waivers somewhat before the button gets pressed. After all, casual handholding a camera can sometimes end up with surprises. Keeping the subject close to the center minimizes this risk but does end up with shots more akin to record keeping that creative composition. Every image will end up looking more or less the same. The subject may vary, but not the composition or the framing.
Aspiring photographers who feel they have progressed beyond this stage though often fall into a different trap known as the rule of thirds. Rather than every image having its subject dead center in the frame, now every subject will fall on one of the expert-approved "power points" where the intersections of the rule of thirds tic-tac-toe board cross. This does help introduce at least some degree of variation in composition since now there are four possible subject locations rather than just the single point in the middle of the frame. But by offsetting the subject this way it can tend to leave a greater amount of the frame to fend for itself. Wherever the subject isn't, the rest of the frame still is, and if one isn't careful it can compete for attention with the intended subject.
The eye tends to be drawn to the brightest or most vibrant point in the frame. All's well if this happens to be your subject. Not so much if this ends up being some random background object instead. This is an unfortunate problem that is thankfully easily avoided. A simple scan of the rest of the frame can alert you to any potential problems. A simple reorientation of your camera position can shift that distraction far enough aside so it lies outside the frame or is blocked so that it no longer competes for attention.
You can place more than one subject in the frame of course. Rather than ensuring that the rest of the frame is free from distractions you can intentionally align your camera position so that something else of interest strategically fills a portion. It's generally best to retain one principal subject even if it is in turn reinforced by secondary subjects. These may serve to repeat the shape or substance of the main subject or they may merely complement it in some thematic way. Whatever your intent, put some thought into your composition before you commit yourself by releasing the shutter.
Perhaps the most distracting thing to keep an eye out for is a distracting element right on the edge of the frame. Neither wholly in the frame nor cropped completely out, such intruders can be troublesome indeed. As the eye scans around the frame they would quite naturally stop at such a distraction to ponder its significance, only to conclude it was nothing before moving on. All this serves to shift one's focus to matters other than the intended subject, yet the entire problem is generally quite easy to avoid. A tiny change of position or focal length is all it should take to either definitively include whatever it may be in the frame or get rid of it entirely by cropping it out. Again, a few moments of attention to such details can be time well spent to avoid noticing such things only too late. Yes, you can crop digitally after the fact, but by so doing you would be wasting some of the megapixels of resolution you paid for when you bought your camera.
And perhaps this is the best way to summarize my entire point. You paid good money for your camera. You ought to strive to get the most out of every pixel in the frame. In other words, maybe there really isn't any "rest of the frame" after all. The whole thing contributes to either helping or hurting every image you take. Make sure you get your money's worth out of the entire frame. Don't let any part of it go to waste.