The Vivre Card is also known as "The Paper of Life". This ordinary looking piece of paper will actually move in the direction of the person who had it made.
The Vivre Cards may appear to be just your average sheet of blank paper, but they actually serves a very important purpose. They are the best way to find those you wish to find in the world.
This paper is only produced in the second half of the Grand Line, also known as The New World. Much like an Eternal Pose is locked to a particular island, these pieces of paper lock on to a certain person who had the paper made. They are made by using fingernail clippings of the person you wish the paper to link to. They are both fire and water proof. Despite this, it can be segmented into as many pieces as possible.
This Vivre Card helps you find the person who had it produced. When left to rest it will gently move on it's own in the direction of the person the paper has been linked but not the distance. No matter where in the world they are. This really comes in handy in the Grand Line, where navigation is difficult.
The card can also show you the condition the person is currently in. As the person's life energy starts the fade, the paper will slowly burn away. When the person dies the paper will disappear, but if the person recovers it will return to it's original form ( Volume 50-CH. 489-490/ Ep. 381).
If a person were to carry more then one Vivre Card from separate people. The most common practice of discerning between the items is to write that person's name on the paper.
The Vivre Card was first seen in One Piece Volume 18 - CH. 159 / Ep. 101, when Ace D Portgas gave it to Luffy. It was never explained what the paper did, other then that it would allow them to find each other. No more was explained, and Luffy didn't ask. To prevent himself from losing it. He asked Nami sews it onto the back of the red ribbon on his straw hat( Volume 18-CH. 160/ Ep. 103).
This paper was not seen again until after the defeat of Gecko Moria, a member of the Shichibukai, on Thriller Bark. Lola of the Rolling Pirates gave Nami a piece of the Vivre Card that is linked to her mother ( Volume 50-CH. 489/ Ep. 381). It was this that reminded Luffy and Nami of the paper that Ace had given him. The name of the paper and it's purpose was unknown to all the Straw Hat crew until this event.
The entire Straw Hat crew was given a piece of a Vivre Card by Silvers Rayleigh, while they waited for the Thousand Sunny to have it's special coating applied in Shabondy Archipelago ( Volume 52-CH. 507/ Ep. 400). The crew is later separated across the world, and these cards are their best hope of reuniting.
While on the island Amazon Lily, in the Calm Belt, Luffy temporarily lost possession of his Vivre Card piece that led back to Rayleigh. It had been taken when his clothes had been removed. After escaping capture, he was able to reclaim this card from Margaret, who had done the alteration on his clothes ( Volume 53-CH. 515/ Ep. 409).
After the misunderstandings had settled in Amazon Lily and he was considered welcome, Luffy soon discovered that his brother Ace had been scheduled to be executed. He examined his brother's card and it had become even smaller then when he last saw it. It was then that he resolved himself to wait to reunite with his crew and instead head out to rescue Ace ( Volume 53-Ch. 522/ Ep. 416). Luffy spent most of his journey on the Marine ship to save his brother either eating or staring at the the ever shrinking piece ( Volume 54 CH.524-525/Ep. 418-422).
Once Luffy had infiltrated the great prison Impel Down. He used the Vivre Card Ace had given him to navigate to his brother's location ( Volume 54-CH. 526/Ep. 423). It can only show him the general direction and isn't of much help through the maze-like prison.
In the anime version the scene where Luffy is given the Vivre Card by Ace was changed to fit the altered events. Unlike with the manga version, where Ace gave Luffy the paper soon after arriving on the Going Merry, Ace traveled with with the Straw Hat crew into Alabasta for some time. Ace had been following what turned out to be a false tip in his pursuit of Blackbeard. When the lead was revealed as a hoax in Episode 101, he gave Luffy the card and left to continue his chase.