Composition is the combination of a variety of techniques that can make and image more appealing to the human eye.
Rule of Thirds:

This is a technique where rather than placing the focus of an image in the centre of the shot, it will be placed off to the left or right instead as it is more interesting and exciting to see. This works because everyday we see our focus is placed directly on what we want to see so taking it out of the traditional way of seeing things can spike interest.
Leading Lines:

This is an attempt to force the human eye to look at a point without the brain really acknowledging it. This is done by using straight, diagonal, curvy (etc.) lines and making them all end at the same focal point meaning no matter where you start on the image you will always end up looking at the focus point.
Symmetry and patterns:

Symmetry and patterns surround us in our everyday life but we don’t pick up on it as often as if we were looking for it. It is a technique that can make architecture, images and many more art forms more appealing to the human eye but it can also be used with slight alterations on each half changing the message of the image on one side compared to the other.
Background:

This is spoken about in more depth when it comes to photography and cinematographers where the background can either isolate the main focus of the image/shot or distract from it. Backgrounds will be made blank so it helps keep the focus on the main image prominent. Sometimes parts of the foreground may be blurred or blanked out so you focus on the background instead.
Depth:
Depth is similar to background but instead the background tends to be shown to be further away by having depth of field applied. This can either focus the vision on a closer object while blurring out the background or vice versa.
Viewpoint:

The viewpoint a photo is taken from can heavily effect the ideas behind the photo and can change someones view on the picture completely compared to if it was taken from another angle or view. Views on a picture can be changed just by changing which angle you take it from whether its from the left or right, looking up or down or just looking straight on, these can all change opinions on an image.