In the ending, Bond survives being handcuffed to the bomb in the Fort Knox vault when a specialist switches it off with seven seconds left, and Auric dies when he is pulled out of a hijacked jet. The bomb is a market play rather than a heist: the villain does not want to carry off the gold at Fort Knox, he wants it contaminated so that it cannot be used, which would raise the value of his own gold.
Oddjob dies in the vault, and the villain tries to get away by hijacking a plane. A fight in the cabin sets off a shot, and the sudden loss of cabin pressure pulls him out of the window to his death. Bond and Pussy Galore then bail out over the sea and share a kiss as a rescue helicopter flies near.
In editorial terms, the ending is easy to follow because each step causes the next: the plan, the countdown, the pressure change and the rescue. None of them needs a lucky break, and it could be argued that this chain is why the finale still reads so cleanly.
The person who stops the bomb is a specialist, not Bond, who is still handcuffed to it when the seven seconds run down. That is an unusual choice for the early series. In Dr. No and From Russia with Love the threat is a person or a plot against Bond; here the threat is a device, and the hero's job is to get the message out so that US forces can arrive. Bond's earlier scenes set this up: the Miami card table and the golf match show him beating the villain at his own games, but the vault is the one place where winning on skill alone is not enough.
The set matters to how the sequence plays. Ken Adam designed the vault because the production could not see inside the real Fort Knox, and the gold in it was shown piled about 40 feet high, while real gold cannot be stacked higher than about 2.5 feet. The audience believes in a vault that no outsider had seen, which is part of why the bomb feels credible. In my opinion, the plane scene is the weaker half on logic but the stronger half on structure: it closes the villain's arc with the same idea, pressure and contamination, that drove the whole scheme.