A Replica (レプリカ Repurika?) is an artificial copy of another being, and a special type of Nobody. The first successful replica in Vexen's first batch is Riku Replica in Kingdom Hearts: Chain of Memories. The first and only replica of the second batch is later revealed to be Xion, (the fourteenth member of Organization XIII), Experiment No. i in the Organization's Replica Program. In Kingdom Hearts II, Vexen will make dark clones of Sora during the optional battles against him. In Kingdom Hearts III, the Replica Program is revived, and Vexen is able to perfect his replica models to act as vessels for hearts.
An empty replica takes on the appearance of a white humanoid mannequin. When a heart or data thereof is placed within a replica, the replica will take on the outwardly appearance of the heart's original physical form.
Replicas (also referred to as "puppets" or "clones" by some other characters) are synthetic copies of other people. While the exact method of creating a replica is unknown as of yet, they have been shown to be able to be created out of different materials. Riku Replica was created using data collected by Vexen from his fight with the real Riku. He believed he was the real Riku due to Naminé's memory manipulation.
Xion, an imperfect replica of Sora, was also made by Vexen and later altered by Xemnas. She was created from Sora's memories, but looked so different from Sora because the memories she was made from took the physical appearance of Sora's most important and strongest memory: Kairi. Replicas, like Nobodies, fade into darkness after they are defeated. Xion, however, was absorbed by Roxas, therefore she continues to live on inside him, and inside Sora.
Most replicas have a mysterious, stoic nature and very seldom give straight answers. Also, a trait shared by all replicas shown in any version of the series is that they are very sensitive about the fact that they are copies. Riku Replica, upon learning he was a replica, constantly referred to himself as "fake" and became obsessed with trying to become a different being than Riku. Xion even refers to herself as a "puppet" after she learns of her existence. In the manga, the Vexen Replicas are very quiet and sad compared to the original Vexen, telling the Riku Replica that "we are all failed replicas.". However, the manga is non-canon.
In Kingdom Hearts III, Master Xehanort's real Organization XIII reinstates Vexen to continue the Replica Program. According to Vexen himself, his new replicas can become real enough to exist as a being in their own right, for example, to serve as "permanent" vessels for the Organization's time-traveling members (Young Xehanort, Ansem, Xemnas, Vanitas and Dark Riku), in addition to recreating Xion based off of records of her existence from Vexen's research. There were also the Replica Xehanorts, which could reproduce the weapons and powers of all the main members of the real Organization XIII, with the exception of Master Xehanort himself.
....even this newfound power! I thought by finding some new strength I could finally be someone.
Replicas seem to have a few unique abilities. Replicas appear to be able to fight as soon as they are created, not needing to learn fighting techniques or become stronger. This is most likely a trait passed down from the person they were created from. Though this only applies to replicas already completed and only need data to finish them; Lexaeus noted that Vexen was "nearly done" finishing the Riku Replica, which took the time Riku spent going through two floors in Castle Oblivion to be completed. The most prominent ability Replicas have is the ability to absorb the life-force of other beings, increasing the Replica's overall power and allowing them to use any unique abilities the being absorbed may have had.
In fact, the main reason for Xion's creation was for her to absorb Roxas and become "the new Sora", thus preventing the real Sora from ever awakening from his sleep. Indeed, Axel confirmed that while Sora was sleeping, the entirety of his power was being shared by Roxas and Xion; though only when Xion made a connection to Sora's heart and siphoning Ven's keyblade out of it in the form of a Kingdom Key. However, this connection was unstable, given Xion lost her keyblade due to Roxas falling into a coma when Naminé started repairing Sora's memory; Roxas would later weaken due to Xion sapping him of strength unknowingly. Also, Riku Replica absorbed Zexion's energy in Kingdom Hearts Re:Chain of Memories, something that was encouraged by Axel. This indefinitely made Zexion fade as his power seeped out, and in turn, this made Riku Replica obtain more power.