People say one key difference between the amateurs and the professional photographers is that the professionals take a lot more pictures. That may be true, but there's another difference. The extra images are typically part of a creative exercise; they aren't random shots.
Ansel Adams once remarked that every now and then he arrived on a scene "just when God's ready for someone to click the shutter." I've had my share of images like that, but more often, I have to work at it.
For me, the process works a bit like this: Something strikes my eye, and I keep refining the composition until the image consists only of the essence of what drew me.