Paopu Fruit

A Paopu Fruit is a star-shaped fruit native to Destiny Islands. It resembles the star fruit. According to legend, "If two people share one, their destinies become intertwined. They'll remain a part of each other's lives no matter what." This gives the fruit great symbolic meaning.

Kingdom Hearts
In an early scene in Kingdom Hearts, Riku explains the fruit to Sora while on the bridge in Destiny Islands. Riku tosses him one and tells him a legend that says that if two people share the same Paopu Fruit, they will remain a part of each other's lives forever. Later on, while racing for the right to name the raft they have built, Riku raises the stakes. He says that the winner should get to share a Paopu fruit with Kairi (though if asked about it after the race, he will state he was merely joking). This intensifies the rivalry between the two, both to prove who is stronger and to gain Kairi's attention. Selphie thinks the legend is very romantic and wants to try it, sometime. Later, in the Secret Cave, Sora draws a picture of himself giving Kairi the fruit. This same drawing touches Kairi in the end credits of Kingdom Hearts (she is seen shedding a few tears) and draws another picture of herself giving the fruit to Sora.

Kingdom Hearts: Chain of Memories
In Kingdom Hearts: Chain of Memories, the fake good luck charm Naminé gave to Sora in Castle Oblivion, also resembles a Paopu fruit. This good luck charm returns to its true form when Sora begins to remember Kairi.

Kingdom Hearts II
In Kingdom Hearts II, the Paopu Fruit is the keychain on Kairi's Keyblade. During the end credits, Sora discovers that Kairi had added onto the picture that he drew in the first game; the picture now depicts Sora and Kairi exchanging a Paopu fruit.

Kindom Hearts Birth by Sleep
Aqua mentions them when handing out Lucky Charms similar to Kairi's to Terra and Ven. She also implies that the skin of one was used in the construction of said charm.

Trivia

 * Quite interestingly, despite its deep meaning to the main characters, no one in the series has shared a real Paopu Fruit as of yet.