Pipes can burst due to corrosion, but in the winter it is more common for pipes to burst due to freezing water. When water freezes into ice, it expands. Don't believe me? Test it out yourself. Put some water in a bowl or ice cube tray in the freezer. The water will expand. The volume of the ice cube will be greater than the volume of water.
If water in your pipes freezes, it will expand. This puts greater pressure on the inner walls of the pipe. If the pressure is great enough, something has to give, and that's the pipe. The pipe expands outward, and cracks, giving you a cracked pipe and a plumbing nightmare.
To avoid bursts pipes you need to keep the water from freezing. Pipe insulation is the best way to do this. If you have an older home, it's more likely the pipes are not well insulated or not as well insulated as newer homes. Keeping pipes away from outside walls can help as well. If you're leaving your home for a few days or weeks in the winter, don't turn off the heat. Turn it down a bit, but don't turn it off. Turning off the heat will result in lower temperatures at the location of the pipes and greatly increase the chance of a burst pipe.