The item appears in your inventory during the fight with vengeful spirit. It is used to bring back one of the characters in your party from fainting. 1 appears when you fight the weak version of Shinozaki and 2 when you fight the strong version of Shinozaki. They stay in your inventory for the rest of the game.
You can find the Resurrection Vial in BAD END-10, there will be three blue spirits in the room before you find the girl's body. Talking to one of them will hand over the Resurrection Vial. It is used to resurrect Shiho or Kaori in the fight with the vengeful spirit.
Significant plot details end here.
The icon for the Resurrection Vial in CORPSE-PARTY ZERO didn't exist in the Japanese version of the game, it was added in the English translation.