A transporter duplicate results when a transporter accident creates two copies of the same person or object. Refraction or reflection of the transporter beam is usually to blame for such duplication.
The duplication may be incomplete, as was the case when James T. Kirk was duplicated in 2266 after a strange ore from the planet Alfa 177 altered the transporter's function. Though physically identical, each Jim Kirk lacked certain personality traits of the original Kirk. The duplication created two distinctly different individuals, a "good" Kirk and an "evil" Kirk; neither copy could function as a complete person. The transporter was used to re-merge the incomplete copies into one functioning individual, reversing the original duplication. (TOS: "The Enemy Within")
The duplicates may be complete copies of the original, not only physically identical but with the original's personalities and memories intact. In 2361, then-Lt. 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")