Apparently all-knowing, she is capable of answering any question. However, the Oracle is bound by one rule: One question, one answer.
In her words, every person may ask her a single question and be answered. Afterwards, the Oracle cannot answer a question to the same person. She refuses to break this rule to Iago, but is more apologetic to Aladdin.
The questions the Oracle answers do not have to be directly at her, as shown when Iago wondered out loud ("VERY loud", as noted by Genie) why the King of Thieves had wanted the scepter which houses the Oracles spirit when there were other seemingly more valuable treasures to steal. Since she heard the question, and as it was indirectly about her, the Oracle declared, "Your question is mine to answer!"
Otherwise, one in possession of the Oracle's scepter can summon her and then ask their question directly to her, as shown when Aladdin did so. In this instance, when he asked where his father was, the Oracle told him how to "Follow the trail of the Forty Thieves".
She can also provide a single additional piece of information regarding the answer. Like when she warned Aladdin that his father was trapped within the world of the forty thieves (and what she meant was Cassim was trapped by his own greedy ambitions rather than an actual prisoner), she also showed the forty thieves the way to The Vanishing Isle when all Cassim asked was where the Hand of Midas was.
Although she was not asked, the Oracle revealed to Aladdin that his father was still alive of her own accord after Aladdin expressed having no one during his childhood. It is uncertain why she offered this knowledge to him, though it may simply have been sympathy.
The Oracle first appears in "The Savior" and is portrayed by Jordyn Ashley Olson. She is in Agrabah, protecting Aladdin, who has become shrivelled and weak as a result of being the Savior. When a messenger comes to ask for the his assistance, she informs him that he is won't be seeing anyone that day. Jafar then suddenly arrives, and the Oracle watches as kills the messenger Emir, turning him to dust. The Oracle pleads with Jafar not to harm Aladdin, who ignores her by telekinetically throwing her across the room, rendering her unconscious. Through unknown means, she ends up in the Land of Untold Stories.
After Mr. Hyde takes over Storybrooke, he summons a dirigible, which contains many of the inhabitant of the land, including the Oracle. When the dirigible crashes, all the inhabitants inside, hide themselves away in the forest. When another Savior by the named of Emma begins seeing pieces of a vision, of a battle to come she is advised by Hyde to follow a red bird, which will lead her to the Oracle. Emma follows it to find the Oracle sitting in the forest, and already aware of her identity. When Emma asks for an explanation as to what these visions mean, the Oracle magically summons a staff, and tells Emma to look at the eyes of the bird on top of it, which begin to glow red. After Emma receives a vision of being stabbed by a hooded figure, the Oracle tells her that she saw is inevitable, and that she will be killed. The Oracle then disappears.
On another night, Jasmine appears, and lets the Oracle know she is safe to come out of hiding. Jasmine reassures the Oracle that her identity still remains a secret. Jasmine then asks if she has completed her mission in finding Aladdin, to which the Oracle replies that she hasn't, though is certain he is in Storybrooke, having foreseen it. She promises to keep at Jasmine's side until they find him.
Emma tries to locate the Oracle, and follows the red bird to see her sitting in the forest. She goes over to her, only to discover she has been killed.