marlinman93-
The basic idea behind dry-firing is mastering the trigger pull and sight picture, without the distraction of blast, recoil, noise, and the flinch that many shooters form as a result. Most competitive shooters that I've talked to dry fire about three or four times as much as they live fire their guns. In theory, and perhaps in practice, this builds a muscle memory for proper shooting basics, improving live-fire scores. You also have a chance to become very familiar with every detail of a gun's trigger pull sequence, again without distraction. The key to making it valuable practice is to do it often, do it right, and concentrate just as much as you would when actually shooting.
When I first posted this, I forgot to include the best reason of all for dry firing: you can't get in any live fire practice. If economics, location, or time prevent you from shooting as much as you'd like, dry fire is better than no fire.