Save the world, become a vegetarian?

All living organisms get their energy from the sun. Plants do this directly, but herbivores eat plants; gaining the sun's energy in chemical form. Carnivores eat other animals, getting chemical energy this way, but essentially all the energy in the food chain starts with the sun.
The problem with this chain is that each step is inefficient. The averge efficiency of energy transfer through food is about 10%.
From the food chain diagram it is easy to see that the higher up the food chain an animal is, the more energy is expended in keeping it alive, in terms of other animals required to support it.

The food pyramid - each block represents the number of organisms at each (trophic) level.

From this, it is no big leap of logic to see that by reducing the number of levels in the ecological pyramid between us (essentially carnivores) and the primary producers (plants), the more efficient we will be at feeding ourselves by becoming primary consumers.
So this is where the vegetarian argument comes in - if we place ourselves on the primary consumer level, instead of secondary or tertiary, we will be able to feed far more of us than before on the same amount of plant matter that was required to feed animals which we then ate. Essentially, cut out the meat part of our diet, and we will be able to feed more people on current agricultural produce.
The meat industry itself is a harmful one in many other ways. This article details the many ways in which farming animals is bad for the environment, from methane release to deforestation.

More information on food chains.