The reason is that at room temperature, water molecules are constantly going into the air as vapor and moving back into the liquid water. When you heat water, you are making the vapor that comes off the water have a higher pressure. When the pressure gets as high as the pressure of the surrounding air, bubbles of vapor can form inside the liquid and push against the air. When this happens, the liquid boils. If you remove the air and water vapor in a vacuum chamber, water vapor can't go back into the liquid. In fact, the vapor going off from the liquid will have enough pressure to actually make bubbles in the liquid.

That's why water will boil in a vacuum chamber. I also told you it will freeze at the same time. Why is this? It turns out that water molecules like to be next to each other in the liquid. It takes energy to move them into the vapor. When water molecules are moving back and forth between the liquid and vapor, the energy that is taken from the liquid to put molecules into the vapor is replaced by the energy returned when molecules move from the vapor into the liquid. In the vacuum chamber, though, the vapor is taken away, so none of the energy is returned to the water. As the water loses energy, it gets colder and finally freezes.