The rule of thirds is a rule that most photographers use. This states that there should be two equally spaces horizontal and vertical lines. By doing this you make sure that the horizon doesn't take up more than half of the page. By doing this it will help keep the proportion of the picture even. This is also used in other types of art, not just the horizon, but it also includes people and other things. It is also to make sure that there isn't just something in the middle of the picture, to keep it even. The best focal points should be at the intersection of one of these lines, with secondary focus on the lines alone.
Leading lines are any line that leads the eye to a different place. This can be a line that leads you into a different spot in the picture, or even out of the picture. Anything with a definite line can be a leading line, this includes many things like a fence, train tracks, a road anything that leads your eyes somewhere else.
Composition is the placement of visual items in a art peace. It is normally known as the organization of elements in a work of art. These can be many different things, and described in many ways also.