The Doctor, desperate to know if Missy and Clara have really been exterminated by the Daleks, must resolve a millenia old conflict with his oldest nemesis, Davros. All the while, Missy and Clara scramble to find their way back to The Doctor and escape the Dalek planet.
SPOILERS AHEAD!
The Witch's Familiar opens with Clara bound and hanging upside down while Missy regales her with a story about The Doctor, primarily to prove a point and finally explain how the "zapped to death" gag actually works. It was pretty obvious they weren't dead, even from the end of the last episode considering we've seen Missy pull that stunt before, only to resurface totally fine. With that question out of the way, the focus shifts to Davros and The Doctor.
The Doctor has no choice but to confront the Daleks and discover if his friends are in fact dead. He then finds an old Dalek blaster and proceeds to chair-jack Davros, riding it into the nest of Dalek soldiers! While hilarious a moment as this is, the object of this image was to plant the idea in our heads that The Doctor is not so different from Davros. Doing donuts with the chair and brandishing the blaster, he did mirror the image of Davros a great deal. Upon returning to Davros' chambers, he presents The Doctor with a choice; a choice he once had to face ages ago in the classic Doctor Who era. He explains that the cables keeping him alive work by connecting to every living Dalek on the planet. If he were to destroy them, it would sever the lifeline to both the Daleks and Davros, killing them all.
He knows that not only is the decision deplorable, but possibly a trick and likely just to prove how equal the two really are, were he willing to commit genocide against an entire species. This is where the proverbial chess match begins between the two. The dialogue becomes an emotional roller coaster. When The Doctor refuses, Davros asks why he even came in the first place. He claims it wasn't shame or anger, it was because Davros was sick and dying and he asked him to come. In the end, The Doctor needs to be a doctor. Its the promise he made to himself. This brought out a side of Davros never before seen. He actually congratulates him and cries. He confesses that he's not trying to turn The Doctor into a monster, he just wants the conflict to finally end. His request isn't out of fury, but mercy.
While this comes as a surprise to us, this turn shakes The Doctor to his very core. Davros is the father of the Daleks and responsible for forging his greatest enemy race. The mere fact that he has grown so weary of the war they continue to fight is a sign of hope for The Doctor. If he can finally bring Davros to a point of truce, albeit on his deathbed, it means one of the darkest points in his life, the battle that never seems to end, will finally be washed clean from his story and bring him the light he's been searching for. Unfortunately, true to fashion, Davros' emotional, heartfelt surrender was a trap! By pulling the cables linked to the Daleks, Davros can feed off his "Timelord Energy" to restore himself and make the Daleks stronger than ever. Luckily, always being a step ahead, he was able to turn Davros' betrayal against him and escape with Clara in tow. The episode ends with The Doctor finally understanding, despite the events that just unfolded, who he is and what promise he made to himself; a promise of mercy. We are once again shown the battlefield with Davros entrenched among the Hand Mines, and The Doctor holding him at gunpoint. He makes the choice, not to kill him, but to instead shoot the mines and save the boy, showing mercy when no one else could.
The overall purpose of this episode wasn't just to wrap up the previous one, but to present a thesis. Mainly, the idea that the all consuming effort to vanquish that which causes conflict in all of us, forces us to match that level of intensity and eventually surpass it to survive. Ultimately, we become that which we dread. The Time War that destroyed the Timelords and the Daleks was over, but the conflict remained between The Doctor and Davros; one always finding a way to overcome the other. They claim to have only ever done what was necessary to survive, but they both fail to realize they're both children of war. They are the same and always have been. The only difference being Davros is searching for an end to The Doctor, but The Doctor is searching for an end to the conflict itself.
