The SRBs are constructed in four cylindrical sections. These have to be sealed together completely to prevent the escape of the extremely hot by-product of the burning fuel during a launch. The O-ring are rubber rings play a vital part in sealing the joints.
On the day of the launch. The weather was unusually cold and this caused the rubber of one of the O-ring on the joint between the bottom two segments of the right SRB to become brittle. This, combined with the faulty design of the escape. The gases and flames burned through the metal that held the SRB in position. When the SRB broke off, it ruptured the side of the external fuel tank. This allowed the liquid hydrogen and oxygen to mix prematurely and this is what caused the explosion.