What does Thanos mean by this?

Question

When Thanos and Gamora are in Vormir, Thanos says this to Gamora:

"I ignored my destiny once. I cannot do that again. Even for you."

What does he mean by that? Specifically:

What was the first occasion where he ignored his destiny?

Answer 1

When he let Titan die

Thanos reveals in the film that he had proposed a plan to save his people by killing off half the population. This process would be entirely random without prejudice between Rich/Poor, Male/Female, etc. When his plan was rejected, Thanos watched his people suffer and die, making him the last or one of the last members of his people.

Thanos: It was. And it was beautiful. Titan was like most planets: too many mouths, not enough to go around. And when we faced extinction, I offered a solution.
Strange: Genocide.
Thanos: At random. Dispassionate, fair. Rich and poor alike. They called me a madman. And what I predicted came to pass.
[...]
Thanos: With all six stones, I could simply snap my fingers and they would all cease to exist. You know what I call that? Mercy.
Strange: Then what?
Thanos: I finally rest. Watch the sun rise on a grateful universe. The hardest choices require the strongest wills.
_{Marvel's: Infinity War - Transcripts Wiki}

After Thanos had gained some power with an army and begun taking over planets and killing off half their population, he began to see the paradises he created, which is when he realised with the 6 Infinity Stones he would be able to turn the universe into a paradise.

His first mistake was therefore not saving his own people, and as such he decided to save the universe.

Answer 2

Although Edlothiad's answer could make sense, I think what he was referring to specifically is left either to interpretation or for the next movie to clarify. He could have been talking about his people.

But from my understanding, Thanos really did try to save his planet, but did not have the ability/power to do it alone, and nobody was willing to help his plan, so of course the plan was never executed. I don't think that qualify as "ignoring my destiny". If that was what he was referring to, I'd expect a wording along the lines of "I failed at executing my destiny once".

What I think Thanos was referring to was simply him saving Gamora the first time. Although everything went down pretty fast, and I couldn't rewind to make sure, I think Gamora was taken from the "about to die" side of her people, when Thanos "adopted" her. Since he obtained the Soul Stone this way, we can be sure that Thanos really loved her, even if many characters would argue otherwise. So my understanding of that scene was that it was the only time Thanos ever made an exception in his plans, to save Gamora, and it was a really significant event in his life. On that day, he ignored his destiny and chose to save one person who he was supposed to kill.

Then, he realizes that on that day, saving Gamora was not a big dent in his plans, just a negligible difference. But this time, saving her requires him to give up on the entire thing, and prevents him from "saving" the universe. He cannot ignore his destiny again, this time the consequences are several orders of magnitudes bigger. Even for her, the only person he loves, he can't make an exception again.

The movie has very strong utilitarism vs deontologism themes (think about the trolley problem). If we ignore the (very likely) theory that Strange gave out the stone because he saw the future and had to, you can find many instances of "good" characters being unwilling to sacrifice people for the greater good (Wanda and Vision, Strange and Tony, Peter Quill and Gamora), which ultimately leads them to fail, while the "bad" character, Thanos, was willing to do what it takes (kill a loved one) for his idea of the greater good. The big theme was that being nice does not necessarily make you win, as opposed to pretty much every other marvel movie. This time, being the good guy was not enough.

Only one side was willing to do whatever it takes to win, so that side won.

So as for your question, Thanos was simply putting in words his very hard decision to sacrifice everything (to him) for his greater good, his destiny. He chose to save Gamora when the stakes were low, but when the stakes get higher, he can't ignore his destiny this time, and chooses to sacrifice her.