A transporter duplicate resulted when a transporter accident created two copies of the same person or object. Refraction or reflection of the transporter beam was usually to blame for such duplication.
The duplication process could result in two incomplete copies, as was the case when both a canine species and James T. Kirk were duplicated in 2266 after a strange ore from the planet Alfa 177 altered the transporter's function. Though physically identical, each copy lacked certain personality traits of the original. One canine was docile, while the other was angry. Testing of the re-integration process on it was successful materialization-wise; however, the creature died as a result of emotional shock.
In Kirk's case, duplication created two distinctly different individuals, a "good" Kirk (lacking willpower and command strength) and an "evil" Kirk (violent and self-indulgent); neither copy could function as a complete person. The transporter was successfully used to re-merge the incomplete copies into one functioning individual, reversing the original duplication. (TOS: "The Enemy Within")
The duplicates could also be complete copies of the original, not only physically identical but with the original's personalities and memories intact. In 2361, then-Lieutenant William T. Riker was duplicated when the containment beam for Riker's transporter signal on Nervala IV weakened due to the planet's distortion field. To compensate, the transporter chief aboard the USS Potemkin created a second containment beam, with the intention of integrating the two. However, Riker's transporter signal made it back without help from the second beam, which was reflected back to the surface, creating an exact copy, Thomas Riker, who was rescued eight years later by the USS Enterprise-D. Unlike the two Kirks, the two Rikers were initially identical but became different individuals as a result of their different experiences. (TNG: "Second Chances")