The mystery being that Clara has died twice, both as a Victorian governess and a futuristic genius. Although the modern-day Clara has no memory of these past selves, Moffat assures us "You will uncover the mystery of Clara in the next eight episodes. All will be made clear. You'll get your answer."
As you are no doubt aware, this run of episodes starts this Saturday with The Bells of St. John, in which Clara and the Doctor face the Spoon Heads, who Moffat says "grab hold of whatever is omnipresent in your life and turn it into a monster."
Moffat said off the companion role:
"[The companion is] the person to whom the story happens. A hero is somebody who saves the day and is extraordinary, and that's the Doctor. For the story to have an emotional connection, it has to happen to somebody. The Doctor himself has to happen to somebody. The companion is sort of the main character — not the hero, but the person whose story it is."Of the Doctor's new companion, he said:
"She has that kind of speed and wit and this unimpressed quality that makes the Doctor dance a bit harder. [The Doctor] works a bit harder with Clara. She's obviously secretly devoted to him, but she's little bit harder to impress… she's tough, she's fast, and she's hard to impress. Of course, he's absolutely devoted to Clara [as well]. That's very much driven by Jenna's particular style, which is a fast, snappy response — from a beautiful girl. There's a real sense of toughness. She can be a real adversary if she wants."