According Snake's unnamed boss in the Magic Kaito case "Blue Birthday," the Pandora Gem is a jewel hidden inside a larger jewel that will glow red under the moonlight. According to myth, if the Pandora Gem is held under the moonlight at the time of the Volley Comet, which passes close to Earth every 10,000 years, then the gem will "cry." Anyone who drinks these tears will then become immortal.
Kaito Kuroba decides to become the Kaitou Kid with the attention of drawing his father's murderers into the open. It isn't until after several high-profile heists, however, that his father's murderer Snake appears, in pursuit of the Blue Birthday sapphire.
Snake shoots Kid and takes possession of what he thinks is the Blue Birthday, but Kid survived thanks to putting the real Blue Birthday gem in his breast pocket. Snake goes to an old-fashioned mansion on the edge of the city, where a mysterious balding man with a mustache praises Snake's work, saying "This jewel could be the one he is searching for." The man then went on to explain what the Pandora Gem is: a jewel hidden within a larger jewel that can be identified because it glows red under the moonlight and will, at the time of a comet, "cry tears of immortality". Kid reveals himself to the two men, and vows to find Pandora before they do and "smash it to bits."
In subsequent Kaitou Kid cases, notably the "Red Tear" case (in which Snake appears again) Kaito is shown to be searching for the Pandora Gem.
The Pandora Gem has never been mentioned by name in Detective Conan. However, the Kaitou Kid has made it clear that he is looking for something and in several instances is shown to hold the gems he steals up to the moonlight before returning them as "not what I'm looking for".