First off, the two reasons for breathing are to bring oxygen into the body, and eliminate CO2. It's not very hard to get enough oxygen, especially once you are underwater, and the oxygen in the gas you are breathing is more concentrated than it is on the surface. But CO2 can be hard to get rid of.
To begin with, many new divers pant from anxiety. Panting is rapid, shallow breathing, and it's very poor for gas exchange. The way the respiratory tree is built, the top part of it -- trachea and major bronchi -- is composed of passive conduits, that don't participate in gas exchange. You have to get air all the way down to the small air sacs, or alveoli, in order to deliver oxygen and offload CO2, and if you are panting rapidly, most of the gas you are moving in and out is only ventilating the passive conduits. This is called "dead space", and rapid, shallow breathing basically just exchanges the gas volume in the dead space. If only 10% of what you pull out of the tank is actually participating in gas exchange, you're going to have to breathe a LOT of volume to get rid of your CO2. This is why people commonly describe a scuba breathing pattern that is somewhat deeper and slower than what you use on land, because that minimizes pure dead space ventilation. This deeper and slower idea, though, does not go as far as skip breathing, which is breathing in, holding your breath for a period, and then exhaling. Skip breathing will generally RAISE CO2, and CO2 makes you both stupid and anxious.
It's also true that you have to breathe ENOUGH to get rid of the CO2 you generate, even if your breathing pattern is absolutely efficient. The corollary, therefore, is that anything you can do to reduce your CO2 generation may permit you to pull less air out of your tank in any given period of time. CO2 is generated by muscle activity (and metabolism in general), so the less you move, the less you have to breathe. But to move less, you have to master stability.
One of the common patterns for new divers is to dive out of trim, and usually feet-low. This occurs because many equipment setups put all the weight low on the diver's body, and also because we are upright, terrestrial creatures, who don't find floating in a horizontal posture to be natural at all. But if your feet are below you, and aimed at the bottom, then every kick you make pushes you upward -- and to avoid ascending, you have to stay negative, so there is an equal and opposite force blocking you from rising in the water column. This means that, for every kick, a substantial amount of energy is being expended to go absolutely NOWHERE! If you can orient yourself so that the kicking force goes straight out behind you, you will move only forward, and you will waste less energy.
In addition, a diver who is not relaxed and stable will often use his hands to try to correct his problems. Hands are terrible underwater -- they're very small and give you very little propulsive force for a given amount of effort. (Think about how easy it is to move your hand through the water, compared with the effort it takes to move a fin!) So if you are hand-swimming, you are using a lot of muscle power to do very little -- and all that effort creates CO2 you have to get rid of.
Another way to cope with instability is to play bicycle -- everybody knows a bicycle is MUCH harder to ride slowly than it is to ride fast. Unstable divers swim, and the faster they swim, the more stable they become. But they see less, because they miss all the camouflaged stuff -- and they blow through gas. Slowing down extends your tank, but to slow down, you have to learn to be stable without swimming.
Proper weighting and effective weight distribution, coupled with good body posture, allows diver stability in horizontal trim, which allows the diver to move more slowly and with greater relaxation. Relaxed divers don't pant. The sum is vastly reduced gas consumption.
