Double tails are a deformity that causes the top section of the body to reflect the bottom. This causes shorter bodies and a much larger top fin. DT bettas should not be bred to other DTs since those spawns often result in large amounts of deformities.
Here are some examples of DT bettas (from bettatalk).
Show bettas are bred for overall symmetry. To achieve this breeders often breed single tail bettas to DT to increase the width of the dorsal (top fin). This blue halfmoon shows that he has DT in his blood by the extra wide dorsal.