Kingdom Hearts is a dense series. Its storyline is widely accepted as overtly complicated, and there are a lot of scattered pieces of information that need to be put together to form a coherent picture of the full series scope. That Kingdom Hearts' story was likely written as the series progressed did not help matters, as many plot devices are expanded and given altered context with new information. Even explaining what Kingdom Hearts is can be a little difficult, due to the series not going into detail on what it is, and what it does.
And then there are the elements that are out of selective importance, only relevant to certain games. A major one of these is the concept of seven lights, which was introduced in Kingdom Hearts 1, long before thirteen darknesses also came into the picture. The plot of Kingdom Hearts 1 can be understood as thus: Sora needs to seal the keyholes of all the Worlds, and must also rescue the seven Princesses of Heart. Sealing and unsealing worlds persist across games, but the Princesses of Heart are a concept that is largely abandoned until Kingdom Hearts 3, at which point it is rendered irrelevant due to story developments. This piece of Kingdom Hearts lore is a relic from a bygone era, but it's still worth expanding on for a better understanding of where the series originally came from.
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Princesses of Heart in Kingdom Hearts 1
The Princesses of Heart are a group of seven girls, consisting of Alice (Alice in Wonderland), Snow White (Snow White and the Seven Dwarfs), Jasmine (Aladdin), Belle (Beauty and the Beast), Cinderella (Cinderella), Aurora (Sleeping Beauty), and Kingdom Hearts’ own Kairi. These maidens are all people with hearts of pure light, totally lacking any darkness and potential for corruption. They are called "Princesses," both as an allusion to the fact that most of them are official Disney Princesses, and because whoever can gather them will be able to summon the Final Keyhole, giving the person access to Kingdom Hearts.
Their story roles in Kingdom Hearts proper are fairly minor. Whether onscreen or offscreen, Maleficent and Ansem, Seeker of Darkness' forces gradually kidnap all of them and bring them to Hollow Bastion. There, most of their hearts are made into a special keyblade that Ansem tricks Sora into using on himself to release Kairi's heart. The Final Keyhole is summoned, and every Princess of Heart but Kairi remains in Hollow Bastion for a little while to keep it partially sealed while Sora works his way back to it. Apart from Kairi becoming a Keyblade Wielder and Belle's hilarious moment of heroism in Kingdom Hearts 2, this set of Princesses doesn't really do much, even when they show up in other games.
Princesses of Heart in Kingdom Hearts 3
The concept of Princesses of Heart is revisited in Kingdom Hearts 3, in which it is revealed that the Princess's status can be passed to other people when destiny dictates as such. Kairi remains a Princess, and joining her are Rapunzel (Tangled), and Anna and Elsa (Frozen). Only four of the seven new Princesses are detailed, as they are simply part of the True Organization XIII's backup plan to form the χ-blade and summon Kingdom Hearts. Elsa and Rapunzel’s pre-existing magical powers also have nothing to do with their Princess status, which meshes with other details to make the mention of Princesses feel a little shoehorned in.
The χ-blade just needs seven pure lights to clash with thirteen darknesses to form, who they are doesn't matter. Just by assembling and surviving the ordeals leading up to the Keyblade War, the Seven Guardians of Light have already played into the True Organization’s hands. Things were going so smoothly that Master Xehanort actually risked killing Kairi and delaying the backup plan just to ensure the final pieces of the χ-blade were produced. After Kingdom Hearts 3's story is complete, it seems that the Princesses are still around as a setting element, but aren't likely to come up again due to the series moving towards whatever Quadratum entails. The Princesses of Heart are treated very strangely as a whole, but they serve their purpose as a distinctly Disney-feeling element in Kingdom Hearts' universe.
Kingdom Hearts 4 has not been confirmed to be in development.