I don't understand why this character is still alive, I thought he had died in another movie. I thought Logan had killed him. Did they resurrect him? Or is he rescued by someone?
In what movie did Logan kill him? That never happens.
Sabretooth first appears in X-Men. In this movie he's a part of Magneto's Brotherhood of Mutants. Near the end of the movie he fights Wolverine at the Statue of Liberty. It's Cyclops who appears to kill him by blasting him off the statue.
He didn't die, however – a scene near the end of X-Men hints at his survival, in X2 his name appears on a list of mutants on Stryker's computer, and he was originally slated to appear in Logan – but we never see him again chronologically in the movies, so I'm not sure where you think you see him again. How he survives is left ambiguous, but he has regenerative abilities, so it's not too surprising.
(Note that Sabretooth does appear in X-Men: The Official Game, a game that covers the events of X2 and X-Men: The Last Stand and apparently is canon with the movies. This game shows that Sabretooth clearly survived the events of X-Men (as I noted above), and does ends with Wolverine seemingly killing Sabretooth. Is this the event you're referring to? Sabretooth doesn't appear after this in the continuity, though, so he might actually have died there. On the other hand, there's not a lot of canon to go on after these events, and as I mentioned he was planned for inclusion in Logan, so perhaps he survived.)
In the prequel X-Men Origins: Wolverine, we see an earlier version of Sabretooth. Near the end of this movie, Sabretooth and Wolverine part ways.
I don't know if I'm lost between the movies but there is something I do not understand, because this character comes out again?
Between what movies? When does he come out again? He never appears again chronologically in the movies after X-Men, although he survived.
Since you tagged your question with logan, I'm going to go out on a limb and assume that you thought the character X-24 in Logan was Sabretooth. He's not; X-24 is a younger and more feral clone of Wolverine/Logan.