Summon Gems

Summon Gems are special items that appear in Kingdom Hearts. They each contain the heart of a creature that had escaped its homeworld's destruction. They can be awakened by the Fairy Godmother at the Magician's Study at Traverse Town, unlocking the characters as summons when done so. The four gems contain the hearts of Simba, Dumbo, Bambi, and Mushu. The only summons that are not obtained from a gem are  Genie and Tinker Bell, who are unlocked after sealing  Agrabah's and Neverland's Keyholes, respectively.

In Kingdom Hearts Chain of Memories and Kingdom Hearts II, summon gems are replaced by summon cards and summon charms respectively.

Kingdom Hearts
After the Heartless were unleashed and devoured countless worlds, a handful of souls escape destruction of their individual homeworlds by living on as summon gems. Simba is capable of doing so owing to his powerful heart, Dumbo due to his strong, pure soul, Bambi thanks to his innocence, and Mushu because of his determination.

Somehow, they are scattered across the worlds but across his travels, Sora manages to retrieve them all. He takes them each to the Fairy Godmother, who uses her magic to awaken the hearts within the gems, returning them to their normal forms. After awakening, they join Sora in the form of summons.

Trivia

 * Leon's possession of Simba's summon gem is a reference to the Griever pendant he wears in Final Fantasy VIII, which represents the leonid Guardian Force of the same name.