First of all, we see in 3D and the pictures we take comes out in 2D so you lose depth in the shot. If you're not careful you'll end up with optical illusions making it appear that things are growing out of peoples heads or bars are running through peoples ears.
For example, in the photo below because the tree is directly behind Brie and she's blocking the trunk going into the ground, it looks like the tree is literally growing out of her head.
Dissecting objects are much like decapitations and cutting off limbs. Some are more glaring than others, but now that I told you about the dissecting tree, you're wondering how Brie was able to walk around balancing that tree in her head. I should have moved her a few feet to my left or I should have taken a few steps to the right and I would have had a picture worth editing. Pay attention to what's in the background and remember the camera will flatten the distance between the objects.
Our minds also allow us to focus in only on the subject of our photograph, especially when we're photographing loved ones, so much so that we lose sight of everything else around. The camera doesn't do that which means if you don't pay attention to everything in the frame you end up with elements in the picture that detract from the final product.
The four of us look nice enough in this shot, but there are objects in the peripheral vision that distract from the photo, ruining an otherwise good picture. Plus we're not properly centered. Luckily, I took a look at the camera display before my son left the room and promptly made him take another, resulting in the shot below.
Better, but still not good enough. You can still see the pillow and part of the picture in the background. Unfortunately, this time, I didn't notice the distractions, but thankfully I was ultimately able to crop away the clutter.
Yes, it's true that there are times you can't do anything about the distractions, but in most cases, changing the point of view from which you're taking the picture or asking your subjects to move can transform an average photo to a stellar shot. In the case of the two photos above, since we were obviously posing for the camera, with a few simple changes, the photos would have been much better. Take the time to look at everything within the frame to determine if there are objects you need to somehow exclude. If you can't move the objects or the subjects, move in close to eliminate as much as possible the distractions. This simple step will vastly improve the quality of the pictures you take.
Take out your camera and look through the viewfinder or LCD and start training yourself to see everything that the viewfinder sees. See the clutter in the background, move closer, change the angle of the camera or move the things out of the way so that the only thing you and others can see in the picture will be the one thing you want them to see.
Step four will be learning about cameras and how to get the most out of yours.