How does boiling remove vitamin C from food?
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.