In military theory it is said that whoever controls the air controls the surface. In terms of tennis, this make sense because by being closer to the net than your opponent you are capable of intercepting shots more easily, you are able to produce more angles, you provide less time for your opponent to react and do not have to come up with elaborate strokes.
Let's take the first concept: intercepting shots. Assume that your opponent represents the top of a triangle and the shots that he's capable of producing represent the two sides. The further back you stay, the more court you have to cover. As you move in, however, the opponent's angle stays the same but the distance that you cover shrinks. The only variable that you have to consider is that the further in you move, the FASTER you have to move.
The second concept is also easy to understand: the closer to the net you are, the more of your opponent's court you are capable of exploiting. For example, from "on top" of the net you can hit the a foot from the net as well as a foot from the baseline. The further back you go, the "less court" you have to hit (it's pretty tough to hit a 100mph drop-shot).
The third concept is also easily understood: by moving in, you take time away from your opponent in which to react. He can hit a shot, but if you move in aggressively to intercept it, you give him less time to recover and react. Your job at the net is, in many ways, to act like a pin-ball machine - to redirect your opponent's shot into an area that he cannot cover. You do not have to over-think the volley; you have to outwork the ball. Don't wait for it to come to you; GO TO IT. This is, unfortunately, the most difficult concept for players to execute because, unlike, ground-strokes, volleys require active participation with your feet. You can't (and SHOULDN'T) wait for the ball to come to you. The bonus is that by working a lot on your net game, you will also be aggressive with your baseline game.
Lastly, don't be afraid of getting passed. It's a bit difficult to get accustomed to seeing the ball go by you when you're at the net (simply because it doesn't happen that often when you're at the baseline), but you will learn to handle it. Remember, mastering the net game is mastering the percentages. The percentages are simply in your favor even if your opponent passes you 20-30 times. The fact is, he will also make more errors and you will also hit more winners. But you have to develop a "taste for blood" early on so that you can pounce on that volley like a lion on a gazelle.