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 an android in her image and transferred her memories into it using a synaptic scanning technique. He made several modifications from that of his earlier androids: skin with the appearance of veins, capillaries, tear ducts, and sweat glands. He also included a feedback processor that sent out a false bio-signal, self-adjusting to mimic human aging. She was programmed to eventually deactivate, her positronic matrix self-destructing, giving her the appearance of a natural death. Tainer was also fitted with an internal supplemental holographic program that was activated in the event of her incapacitation. The program responded variously depending upon the identity of whomever was accessing it.
Soong designed Tainer to be unaware of her android nature, initializing her consciousness to pick up from the point of the attack on Omicron Theta by the Crystalline Entity that had left Juliana O'Donnell in an irreversible coma. Soong programmed Tainer to shut down in the unlikely event of her android nature being discovered. The relationship between Soong and Tainer continued for a long, but unspecified period of time, souring when Soong became too focused on his work. Tainer 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 Tainer were reunited, although Data was unaware of her possible role in his life as his formative memories of those days had been erased. Although Data was initially uncertain about how he should feel about Tainer's claims regarding her role in his initial design and early development, a conversation with Geordi La Forge convinced him that he should not avoid Tainer due to his inability to remember her. From this point he began to spend time with Tainer, addressing her as his mother. Data and Tainer bonded over their mutual creative outlet, Data playing violin and Tainer, the viola. Tainer shortly revealed that she was 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 as an android was discovered. Data noted that he had observed clues about her android nature before this point, as her blinking pattern was based on the same pseudo-random sequence that Soong had used for his own, and her viola performance was identical to her practice.
Data interacted with the personalized version of the holoprogram Soong designed to activate in the event that Tainer's android nature was revealed. From this, Data chose not to reveal Tainer's status as an android to her. Data's decision regarded the happiness he believed Tainer obtained from her false belief in her humanity. Data prioritized this over whatever satisfaction he may have received in the shared knowledge of their android nature. Before Tainer 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 object of that love. (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.