What killed this character in Episode VIII?

Question

At the end of Star Wars Episode VIII: The Last Jedi,

Luke Skywalker becomes one with the Force.

He looks quite exhausted after the encounter with Kylo Ren.

But what exactly killed him?

Answer 1

Luke over-exerted himself.

This Jedi had not moved since dawn. During that time, the mountain had quaked. A cliff had crumbled. The twin suns had begun to set. The moon had gone on the rise.

It had taken all his strength to do what he had done. The salt lines of tears on his face showed the incredible strain. Now that it was done, he could enjoy a few last breaths from the island that had been his home.

_{^{Last Jedi: Junior Novelisation}}

His efforts drained his "essence". Ben Kenobi then encouraged him to become one with the Force.

On the ledge overlooking the sea, Luke Skywalker floated a few centimeters above the stone. Pebbles hovered around him. His eyes were closed and his legs crossed. His face was strained, and beneath his gray beard the tendons of his neck stood out. Tears streamed down his face as he poured his strength, his very essence, into the Force.

Behind him the peak shuddered, shedding dust and chunks of debris.

...

Luke heard the wail of the wind and the cries of the birds. He heard his own faltering breaths as he struggled to get up, and the rhythmic thumping of his heart in his chest.

And he heard a familiar voice. Maybe it was real, or perhaps it was just in his memory.

Let go, Luke.

He did and his body faded away, leaving the ledge empty. In the spot where he had been, the Force rippled and shivered. But a moment later this disturbance was lost amid countless other currents of an autumn evening on the island, and the Force continued as it always had, luminous and vast and eternal.

_{^{The Last Jedi: Official Novelisation}}

The film's Movie Storybook also offers this version of events, suggesting that he's taken energy from the Force as well as giving his own strength.

Back on Ahch-To, Luke faded away on the meditation ledge, becoming one with the Force.

It had taken everything he had to project so much of himself onto Crait. Drawing that much power directly from the Force had consequences. But Luke was happy to pay them. His final act had saved Leia, Rey, and the Resistance.

The Jedi would continue, even though Luke would be gone.

Answer 2

He metamorphosed into a Force-Ghost

This scene was the climax of Luke's journey. He has always wanted to be at one with the Force, to avoid conflict and achieve peace.

You'll remember in the little-known movie Star Wars Episode IV: A New Hope where Old Ben (Obi-wan) Kenobi did the same thing when faced with Darth Vader:

Old Ben: If you strike me down, I shall become more powerful than you can possibly imagine

*Gets struck down*
*Turns into air*

Luke has reached the final stage of his journey, he has ushered in a new wave of Jedi (whether he likes it or no), has defended and protected his most precious: his twin sister, Leia and the Rebellion; and has finally brought hope to those who need it most.

He then joins the ranks of Obi-wan Kenobi, Grand Master Yoda, Anakin Skywalker, and Qui-Gon Jinn and has finally become a Force Ghost.

But what did kill him?

I wouldn't say that his encounter with Kylo Ren and his super-force-projection was what actually killed him. Yes, it drained him, but he did recover and prop himself up onto the rock seat again.

From what we can tell about Force Ghostism, is that it seems to be a voluntary act. Those who have become Force Ghosts seem to give themselves in to their final state. Luke completed his encounter with Kylo Ren and his successful mission on Crait, propped himself up onto the seat, mustered the remaining reserves of his energy and let himself go.

Answer 3

Earlier in the movie, when Kylo has a telepathic conversation with Rey, he first thinks it might be a Force projection, but he dismisses that idea because the effort across galactic distances would kill her.

This seems to be the technique Luke used, and it is probably the thing that killed him.