Clara is basically dead. In Hell Bent the Doctor takes her in the moment before her death and escapes in a stolen TARDIS. However, Clara no longer has a pulse. The Doctor then runs into Me at the end of universe (which he assumed would free Clara). Me chastises the Doctor for trying to save Clara from her fate.
The Doctor tries to erase Clara's memories of him, to at least let her lead a new life somewhere else, but Clara reversed the process and The Doctor had his memories of her largely erased. Me and Clara drop The Doctor in Nevada, which is where the episode happens, and he pours out to Clara (not recognizing her) his regret. She leaves him there, with his own TARDIS. Thus we get to this scene (note that Ashildr is only called Me in this episode)
ASHILDR: Still no pulse?
CLARA: Time isn't healing. I am still frozen.
ASHILDR: You know what that means?
CLARA: It means my death is a fixed event. The universe depends on it happening.
ASHILDR: I'm sorry.
CLARA: Why? Why does everybody think I am so scared? We all face the raven in the end. That is the deal. If I go back to Gallifrey, they can put me back, right? On Trap Street, the moment they took me out?
ASHILDR: Of course.
CLARA: Mind you, seeing as I'm not actually ageing, there's a tiny little bit of wiggle room, isn't there?
ASHILDR: Wiggle room?
CLARA: Wiggle room. Yeah, you know, wiggle room. We could, er, you know, stop off on the way.
(Clara sets coordinates.)
ASHILDR: Where are we going?
CLARA: Gallifrey. Like I said, Gallifrey. The long way round.
(The American Diner whizzes through the Vortex.)
The episode ends with the TARDIS Clara and Me are in going off into the universe.