The Obsidian Goblet is a secret item found inside a shattered display case in the Silent Hill Historical Society in Silent Hill 2, and is required for the "Rebirth" ending. It can only be unlocked after completing the game once.
The Obsidian Goblet is a blessed item of the Order. It is necessary for many rituals, including the Holy Assumption and Rebirth ritual. It is an ancient-looking goblet made of pure obsidian, with a snake carved into its stem.
Silent Hill 2: Born from a Wish
The Obsidian Goblet is referenced in the Born from a Wish scenario. The goblet isn't physically collected, but represented by a black board. Maria must collect the black board (along with three other boards representing the three other items) in order to solve the Acacia Key Puzzle.
Silent Hill 4: The Room
The cup is also mentioned in Silent Hill 4: The Room in the Crimson Tome. The tome says that one must gather the "Black Cup, the White Oil, and the Blood of the Ten Sinners". The goblet is on the ritual table in the secret room with Walter Sullivan's corpse.
Silent Hill: Book of Memories
The goblet is also mentioned in Book of Memories in a specific note that speaks of the Ritual of the Holy Assumption.
It is also an artifact, described as, "A polished silver chalice with religious etchings along its base."