“The impossible girl” is a moniker bestowed on Clara by the Doctor due to the bizarre and timey-wimey way he meets her. Before meeting the Clara being apped in London in 2013, he encountered two other girls that shared her voice and her face and that had sacrificed themselves to help him defeat his foes. The Doctor is vexed as to how the same woman could live and die three times and how he, by chance, met her three times as well. These echoes, while obviously sharing Clara’s face and voice, also share her many of her personality traits, though some are exaggerated or downplayed depending on the echo.

The first girl he meets is Oswin Oswald. Oswin is presumably from the far future as she works with children on an intergalactic cruise ship. She has taken this job because, like Clara, she wants to travel and travel in her time is going out and seeing the stars. Unfortunately for Oswin, her first time out in space the ship crashes on a planet asylum housing the Doctor’s greatest enemy (the Daleks) and Oswin is left trapped in an escape pod for a year.

Then one day, the Doctor shows up to solve the problem of a hole in the force field of the planet. This forcefield keeps the Daleks (and so Oswin too) from escaping. Using the computer systems of her escape pod, Oswin guides Amy, Rory, and the Doctor through the maze of the Asylum of the Daleks. Oswin is shown to be sassy, like Clara, though a less wry and more flirtatious than the original. She’s also a complete computer genius, able to hack the Dalek systems with ease, which is likely a reflection of the computer skills the original Clara gained. Like Clara, she doesn’t outright trust the Doctor, and makes him come to get her instead of trusting that he would wait for her to come to the teleportation pad that would get them out of the asylum.

However, when the Doctor comes to find Oswin, he discovers the terrible truth: Oswin had been captured and turned into a Dalek. However, the truth was too terrible to bear so she convinced herself that she was still in her little escape pod. However, showing the same strong will that the original Clara does, Oswin fights off the Dalek conditioning and saves the Doctor by erasing him from the memories of the Daleks and tells him “Run you clever boy and remember me" before sacrificing herself to destroy the planet along with the Daleks. It is later revealed that the name Oswin comes from modern Clara thinking up a username on her computer; “Clara Oswald for the win” becomes “Oswin”.

Years later, the Doctor encounters another girl with the same face as Oswin in Victorian London. However, as he only communicated with Oswin through the speakers in the Asylum, he doesn’t recognize their similarities at first. Only the audience can make the connection that the two women share a face.

Victorian Clara is a tenacious dreamer. She leads a double life as a barmaid and a nanny for children who lost their mother (just like Clara does). When she and the Doctor encounter alien snow, she chases after him, trying to figure out who this mysterious man is. But at this point in time, the Doctor has experienced the devastating loss of Amy and Rory and is not interested in fraternizing with Victorian Clara.

The Victorian echo is curious about the world around her and constantly asking questions but to a much larger extent than the original. While the Clara initially is confused by the Doctor and takes a bit to agree to speak with him, Victorian Clara chases him down to demand answers (though in the original’s defense, the Doctor just shows up randomly at her doorstep). She is a little more open than the original Clara and doesn’t use the wry wit to keep a distance between herself and others, which allows her to connect with the Doctor during a dark period. Like the original, she is also very clever and resourceful, able to pass multiple tests that the Doctor and his friends push on her to make her prove her investment in the Doctor and being a companion. Her tenacity and courage pay off when she stands up to fight a monster with the Doctor and he is impressed enough that he finally accepts her and invites her to come along with him.

Unfortunately, once again, the echo is killed in her attempts to help the Doctor. And as she fades, once again she repeats the phrase, “run you clever boy and remember.” At that moment, the Doctor makes the connection to Oswin and decides that Clara is “impossible” in that she is the same woman now twice dead. He goes in search of another Clara and so meets the modern Clara when she accidentally makes a phone call to the TARDIS.

The issue of the “impossible girl” initially drives a wedge between Clara and the Doctor. He calls her such a name, but doesn’t reveal to her that he’s met her twice before and subsequently why he is so interested in her. This frustrates Clara as she feels like he is keeping a secret from her that she deserves to know. She also can’t help but feel that she is a replacement for somebody else. And so she is left a little weary of the Doctor. She fancies him, but can’t quite bring herself to trust him because she knows he has an agenda that she can’t quite figure out.

Once, the Doctor accidentally admits that he has seen her die before and confesses that she was in the Asylum and in Victorian London and that he believes both those women are Clara. At first, Clara is confused and disturbed by this notion that the Doctor has met her before but eventually comes around and reconciles with the Doctor and lets her anger go, instead deciding that she also wants to solve this mystery along side him. Unfortunately, her memories of this experience are erased due to time loop.

These echoes and her destiny as the impossible girl come to a head when she and the Doctor travel to Trenzalore, a planet that is the site of the Doctor’s future grave. They are greeted by the Great Intelligence, the same creature that the Doctor and Victorian Clara fought and that attacked Clara in the wifi on the day she met the Doctor. Old memories begin to surface and Clara suddenly remembers being told that the Doctor met her in the Dalek Asylum and Victorian London.

The Great Intelligence enters the Doctor’s time stream and scatters himself within it, changing the Doctor’s past so his victories become defeats. The Doctor begins to die at every point in his history, including the Dalek Asylum and Victorian London. Those words make Clara realize what has happened and what she must do. She is the only one who can do it because, in a sense, she has already done it. It gives her resolve because suddenly everything that was confusing makes sense. She now understands why she and the Doctor met under such strange and impossible circumstances and why there had been tension between her before. Thus she jumps into the time stream and is torn apart, but she accepts this as her destiny as the impossible girl. Declaring herself “born to save the Doctor” gives her confidence even as herself, the original Clara, is eroded away.

By entering the time stream, she is torn apart and scattered throughout the Doctor’s timeline into various echoes including Oswin and Victorian Clara. These echoes all eventually encounter the Doctor and save him from various dangers, but also unfortunately appear to die in the process. Clara herself, is deposited at the end of the time stream, lost and confused and unable to remember who she is.

Thankfully, the Doctor comes to give her a piece of her own personal past which helps her remember who she is and to save her and bring her home. This experience solidifies Clara’s relationship with the Doctor. She is no longer weary of him do to any perceived secrets. She has now seen his past and understands him much better than before. This allows for them to have a much more fun yet intimate relationship in the following episode. There’s no hint of tension or mistrust. In fact, this understanding that Clara now has of the Doctor as a person, allows her to give him guidance and encourage him to make a better choice than he did in the past. While the Doctor was a bit of a mystery before, they now can understand each other and function as a near perfect team.