At the end of Pirates of the Caribbean: Dead Man's Chest, we see Barbossa reincarnated. Is there any in-movie explanations of how that was possible, since he was shot cleanly through the chest at the end of the first movie? If Tia Dalma was responsible, does that mean she had the power to make anyone come back from dead?
In-movie, there is no specific explanation as to just how Barbossa was resurrected. Similarly, as far as I can find, there is no explanation in any of the side-story books that were written.
When we first meet her, Tia Dalma is presented as a Voodoo priestess having performed numerous acts related to the supernatural - specifically mentioning providing Jack with his compass.
In truth, Tia Dalma is really the goddess Calypso bound in a human body, so many of her "Voodoo priestess" powers may actually be powers as a goddess.
Whether or not she can "resurrect anybody" is unclear. For instance, Barbossa had been killed, while Jack had been banished to Davy Jones' Locker. Barbossa's soul was not judged by Jones as he had been killed on land. Even with her available powers, she could not retrieve Jack without help. The below quote implies that if they are actually dead and fully crossed over, she would be able to resurrect them.
Pintel: No one said anything about cold.
Ragetti: I'm sure there must be a good reason for our suffering.
Pintel: Why don't that Obeah woman bring Jack back the same way she brought back Barbossa?
Tia Dalma: Because Barbossa was only dead. Jack Sparrow is taken body and soul to a place not of death, but of punishment, the worst fate a person can bring upon himself stretching on forever. That's what awaits at Davy Jones' locker.
Ragetti: Well, I knew there was a good reason.
At the end of Pirates of the Carribean: The Curse of the Black Pearl, there is an after-credits scene that shows Barbossa's pet monkey (Jack) take one of the coins from the chest, which then curses the monkey again.
Now, perhaps the monkey gave the dead or dying Barbossa the coin for him to be cursed again, therefore being able to survive or be resurrected.
Another answer suggested that Barbossa was given the coin to be cursed again, but that makes no sense. If it was the case that everybody who touches the coin becomes cursed then Elizabeth and Will Turner should have been cursed. Since neither of them were, the only explanation left is that Tia Dalma or Calypso used her powers to bring him back.
What about "the world's end" in that movie. We have seen they found the way to the world's end and then bring Jack and Black Pearl back. Now at the end of this movie, Jack said something about an appointment at the horizon. Maybe he will find the way to the world's end again and bring Barbossa back.