It's generally known that boiling vegetables removes a large fraction of vitamin C, but in what way?
Does the high temperature destroy it?
Is it merely absorbed by the boiling water?
It isn't really "absorbed" by the boiling water; more precisely, it is leached into the water. As kiamlaluno said, Vitamin C is water soluble. An important thing to note is that the leaching of vitamin C into water, by itself, doesn't destroy the vitamin C. It's still there; it's just in the water rather than the vegetable. If you consume the liquid you cooked in, you'll reclaim some of the "lost" vitamins.
High heat can reduce the vitamin C content of the vegetables, and when heat and water are combined, as they are in boiling, you can see significant reduction of vitamin C. (One study found that boiling reduced the vitamin C content in broccoli by 45 to 64 percent.) This is because the vitamin is first leached out of the food into the water, and then degraded by the heat. Heat alone will cause some reduction in vitamin C, but not as much as when combined with loss of nutrients through leaching. Steaming and microwaving are recommended cooking methods for preserving as much of the nutrient content as possible because they involve minimal exposure of food to both water and high temperatures.
Actually, vitamin C degrades with heat. The following, by dietician Jill Irvin, says it all:
Vitamin C is one of the least stable of all vitamins in solution and is oxidized readily in light, air and when heated. It is also water soluble. This means that heating in water, (like cooking broccoli in boiling water) causes the vitamin to leach out of the food into the water and also to be oxidized, first to dehydroascorbic acid and then to diketogulonic acid. This last compound has no Vit[amin] C activity at all and is irreversible.
She goes on to say that normal cooking doesn't affect levels of the vitamin too much, but the main issue being queried here is how boiling removes vitamin C from food, and this quotation tells how that happens.
Since Vitamin C is a water soluble vitamin, boiling the vegetables cause the vitamins to get dissolved in the water.