Some people asked me to do a tutorial on composition, and I'm way overdue, so here it goes.
Part 1: What is composition?
Basically composition defines where your attention goes. Generally it's the shape that forms if you outline all the attention points in a piece. So technically, every image has a composition. But not every piece has an eye-pleasing composition and not every image achieves the goal of bringing the eye of the viewer to the right places.
Theoretical example: suppose you have a girl and a lot of birds in the image. They are somewhere in a room full of books. You want the viewer to look at the girl and then notice the birds. If you have a proper composition, that will happen. If not, the viewer will notice the books, the room, get distracted and pass over the girl. He won't get the clear message of the needed attention points right away. And those few seconds he's confused and not understanding where to look at - those are usually whe