Teeth can decay when bacteria and food particles form plaque on the surface of your teeth. These bacteria produce an acid that eats away at the calcium in the tooth's enamel and leads to the formation of minute cavities. If left untreated, the acid will eventually erode through the enamel of the tooth, and begin eroding the dentin beneath it.
This situation is especially undesirable since the dentin is more porous than the enamel and thus, decays at a much faster rate. A large cavity can form under the face of the tooth with little or no visible signs.
If the decay is allowed to progress further the bacteria migrates through the porous dentin and infects the pulp of the tooth. When your body launches an immune response to the infection, the blood vessels around the tooth enlarge and press against the nerves entering the tooth causing the tooth to ache.