Juliana Tainer was a female Soong-type android and geologist in the 24th century. Built in 2338 on Terlina III, she was a replica of the Human Juliana O'Donnell, who died from injuries she received from an attack by the Crystalline Entity on Omicron Theta. She was married to her creator, Noonian Soong and, later, to Pran Tainer on Atrea IV.
In a last attempt to preserve his wife's memory, Soong built a new android in her image and transferred her memories into it, using a synaptic scanning technique. He also made several modifications: skin with real veins and capillaries, tear ducts, and sweat glands. He also included a feedback processor which sends out a false bio-signal, which changes appropriately as she aged through her aging program. She was also programmed to eventually deactivate and self-destruct her positronic matrix, essentially giving her an eventual "natural" death. Finally, Soong created a holographic program to explain to others about her nature, with additional programs for different recipients, and stored it inside her.
Tainer was unaware of her new state of being, believing herself to be the Human Juliana and having recovered from a major injury. Soong deliberately designed the android to be so, and programmed her to shut down in the unlikely event of her android nature being discovered. She lived with him for a long time, but the relationship between the two soured when Soong became too focused on his work, and Juliana left Soong – something that Soong noted the 'original' Julianna would have done as well. She eventually made her way to Atrea IV, where she met and married the Atrean scientist Pran Tainer, becoming his assistant.
In 2370, the USS Enterprise-D arrived at Atrea IV to assist in planetary core experiments. Data and Juliana were reunited, although Data was unaware of her contribution to his design, as his memories of those early days had been erased. Although Data was initially uncertain about how he should feel about Juliana's return to his life, a conversation with Geordi La Forge convinced him that he couldn't 'hide' away from Juliana simply because he was uncomfortable with the change she represented, prompting him to begin spending time with his mother. Although the two bonded over Data's creative outlets such as his violin playing – Data noting that he felt most Human when he was exploring his creative side – there were still some awkward moments between them, including Juliana's revelation that she had actually been responsible for leaving Data behind on Omicron Theta because she was afraid of him turning out like Lore.
During the mission, Tainer was injured, and her true nature was discovered – although Data noted that he had observed other clues about her nature earlier, such as her ability to perfectly play the same viola piece the same way on separate occasions, or her blinking pattern being based on the same pseudo-random sequence that Soong had used for his own.
After viewing Soong's holoprogram, Data chose not to reveal Tainer's true nature to her, concluding that it was more important for her to live a happy life believing herself to be Human rather than take away from her the goal that he had sought all his life simply to give himself something he could share with her. Before she departed, Data told her that Soong had once told him that he only ever had one great love in his life, expressing his certainty that she was the woman in question. (TNG: "Inheritance")
Background information Edit
Juliana Tainer was played by actress Fionnula Flanagan and doubled by stuntwoman Christine Anne Baur. One of Fionnula Flanagan's costumes from "Inheritance" was sold off on the It's A Wrap! sale and auction on eBay. . Christine Anne Baur's Juliana Tainer costume was also sold off on eBay. 
In the script of "Inheritance", the character was described as "a fiftyish [Human] woman dressed in Atrean fashion."  The name "Juliana Tainer" was chosen by co-writer Dan Koeppel, after mountain bike racer Juli Furtado. 
The novel Immortal Coil establishes that Juliana eventually did seem to die in the year 2374, only to be reactivated with full knowledge of who and what she was by the immortal known as Flint. In the novel Cold Equations: The Persistence of Memory, Data learns of Flint's role in reactivating Juliana, deciding to try to find him so that Flint might help Data reactivate Lal.