The Sacred Gems are mysterious gems in each area of the city. Though they are rumored to protect the city, it's unclear how significant they really are, due to their prominent location out in the open and their lack of any visible effects against the Nevi or Gravity Storms.
Alias manages to steal several of them before being defeated, but it's unclear what he planned to use them for. Syd makes candy fakes in order to fool Alias into taking the wrong one but it doesn't work.
They do not reappear in Gravity Rush 2 and are not even mentioned, though the statues that held them are still there.