Living in a Temple deep in the forest far from mortal eyes, where through her magic she could see across the ages, able to read the fates of all who lived, never interfering that is until a unique soul caught her attention. The Soul of the Hero of Legend, eternally reborn when Hyrule's need is greatest. Through her powers she should have seen that Link was bound to that of Princess Zelda, instead she saw only a soul unlike anyone she had ever known, eventually falling in love with the Hero. Preoccupied with her unrequited feelings love for the Hero, a fragment of the darkness, locked in its prison, saw an opportunity to corrupt the sorceress. Its whispering darkness wormed its way into her heart, pushing the light away and warped her curiosity into a desperate desire to possess the Legendary Hero's soul. Of course the evil had its own desires, to use the Triforce to resurrect itself and conquer Hyrule once again. Having pushed the light from her heart, the darkness compelled her to open the Gate of Souls, the doorway to Time itself. Monsters from across the ages pour through the gate to bring ruin to the land of Hyrule once more. As a result of these events, her soul was separated into two beings: The "Light" became the White Sorceress, Lana and darkness corrupted Black Sorceress, Cia.
The Guardian of Time appears as an alternate outfit/skin for Cia and Lana. Outside the DLC, the Guardian of Time only appears in a cutscenes telling the story of her corruption as stylized drawings. The Guardian of Time's true name (if any) is unknown.
The Guardian's role is largely the same in Hyrule Warriors Legends.
In Hyrule Warriors Legends, during the battle against Dark Cia and Phantom Ganon, a dying Cia redeems herself and joins forces with Lana, Link, Tetra, and King Daphnes to defeat the evil that threatens both Hyrule and her life. Following Phantom Ganon's defeat, Cia is saved by the Triforce of Power and together with Lana, Zelda, and Link restores Hyrule to normal with the power of the Triforce. Lana and Cia return to the Valley of Seers and take over their former self's role as the twin Guardians of Time, sharing the Triforce of Power between themselves. In the stylized cutscene at the end of Hyrule Warriors Legends, Lana and Cia appear to even adopt the Guardian's attire though Cia's is purple in color.
The Guardian of Time Costumes from Hyrule Warriors for both Lana and Cia can be unlocked on the Master Quest Adventure Map (which is unlocked by completely the Great Sea Adventure Map).
There are two weapons in the game that where apparently once owned or associated with the Guardian, the Guardian's Scepter used by Cia and the Guardian's Gate used by Lana. Interestingly both are classified as Level 2 weapons, as the Guardian's Scepter is Cia's Level 2 Scepter and the Guardian's Gate is Lana's Level 2 Summoning Gate. Another interesting connection between the two weapons is that Cia's Guardian's Scepter features a Guardian's Gate in its design.
It is possible the Guardian of Time is partially based on the Triforce Keeper from Zelda II: The Adventure of Link as both characters seemingly watch over the Triforce and have the ability to summon Dark Link.
Goddess of Time
Another possibility is the Guardian of Time is based on or meant to be the Goddess of Time mentioned in Majora's Mask. Considering that she is known as the Guardian of Dimensions, it is possible that with her power she may have aided Young Link during his adventures in Termina, which would make sense given that she eventually fell in love with the Spirit of the Hero and there are statues of Young Link in the Temple of Souls. Though she may not have intervened in events in Hyrule, the same may not be true for Termina and she may have saved Link to prevent the loss of the Triforce of Courage (as its destruction could endanger the Light World, given what happened to Lorule after the destruction of its entire Triforce), which may have been in his possession at the time. Of course, given the game's non-canon nature, it is more likely that the Goddess of Time may have simply been a source of inspiration. Of course, the Guardian of Time could be the incarnation of the Goddess of Time within the non-canon universe of the Hyrule Warriors series (which takes place in another universe, separate from the canon series).
Interestingly, the Guardian of Time's split into good and evil counterparts is very similar to the Dragon Ball series characters Kami and King Piccolo, who were also originally one being before splitting into the good and evil counterparts. Another interesting similarity, is the name of their original self is unknown, just like the Guardian of Time, who is only known by her title.