Spoilers from the Season 7 finale of Game of Thrones, "The Dragon and the Wolf".
In one of the final scenes, Jaime and Cersei are discussing Jaime's future with them, at which point
Cersei nods her head, signaling the kill order for 'The Mountain', yet 'The Mountain' pulled out his sword but why didn't he kill Jaime?
Our good mate Nikolaj Coster-Waldau (the actor who portrays Jaime) breaks this down for us nicely in a recent interview with Leigh Blickley on HuffingtonPost:
[Leigh] Not going to lie, I thought this might have been your demise. The Mountain was ready to kill you! But you called her bluff.
[Nikolaj] Cersei had the chance with both her brothers to kill them and she was threatening to do so, but both times she eased off on the trigger. I get that with Tyrion she was setting him up for failure ― making him believe that he was the hero of the day, that he negotiated this amazing support from the Lannister army and what a wonderful thing he did. So that makes sense. For Jaime, I would think he would think there was part of her that still understands that he really is the last person that she has. That is the truth; that must resonate somewhere inside her. That would help. Or maybe the Mountain is just so thick that he didn’t get the eye signal. Maybe there’s a scene right after where she goes, “Why the fuck didn’t you kill him?! I gave you the signal!” I don’t know. Who knows. We’ll never know because that scene isn’t there, but that might be the case.
-HuffingtonPost, Nikolaj Coster-Waldau Breaks Down That Huge Jaime Moment On 'Game Of Thrones'.
The caveat is that this is the actor's own interpretation of the scene, but that goes to show that the writers haven't told Nikolaj the actual reason for this. That's not to say that one doesn't exist, however, this is all the insight we have at this moment.
I am not sure whether citing the leaked scripts is a good idea. But, as the episode is already aired, here is the line from the leaked script:
[Jaime and Cersei]: "He walks out on her, while she is threatening to have The Mountain kill him. Jaime calls her bluff however, and the Mountain stands aside and lets him leave her chambers. Next we see him he's on his horse heading north. That's all we see of him."
So, Cersei was bluffing, and probably that wasn't her “Go Ahead” nod, and only Ser Clegane knew.
The order we see on screen is Cersei telling the Mountain to draw his sword. The kill order never comes. This is confirmed in the official script.
JAIME: Give the order, then.
He watches her and waits.
The Mountain waits for a command from his queen.
She nods. The smallest possible nod.
The Mountain draws his sword.
Jaime knows there’s no point fighting. He knows he will be cut in half.
He stares at his sister for a long beat.
JAIME: (quiet) I don’t believe you.
After a long beat, Jaime turns and walks away, right past the Mountain and his drawn sword.
Cersei watches. She does not give the command.
Game of Thrones, Season 7 Episode 7, "The Dragon and the Wolf"
You can see Ser Gregor being given instructions earlier in the episode on what to do if anything bad happens "Kill the silver haired bitch first then... etc". So the big zombie-knight can follow basic instructions. "If I nod to you-take out your sword, but don't kill him" would be just as easy.
