Gum tissue bleeds due to inflammation. Inflammation is caused by an accumulation of bacteria (which is normally in the mouth) and food debris. This combination is called plaque. As the bacteria use the energy of food to multiply they produce materials that are toxic to the gum tissue. It is this process that starts the inflammatory response by the body.
In order to do this, the circulation is increased where the plaque builds up and we end up with red swollen gums that bleed easily when you brush. This is why the dental community stresses brushing and flossing. In combination, they will minimize the amount of plaque around the teeth. It really works.