The Arrow of Apollo is a great hunting arrow and a symbol of Apollo, Lord of Kobol.
Legend states that the Arrow is the one surviving clue to location of the planet Earth (Kobol's Last Gleaming, Part II). According to accounts of the scriptures of Pythia and Laura Roslin's statement to the Quorum of Twelve, the arrow is a key of sorts, which will open the Tomb of Athena (Fragged).
This arrow itself was on display in the Delphi Museum of the Colonies in the City of Delphi on Caprica (Kobol's Last Gleaming, Part II).
While the city itself suffered extensive damage as a result of bombing during the Cylon attack, the Arrow survived undamaged. It becomes the focal point of Laura Roslin's attempts to discover the whereabouts of Earth following the apparently accidental discovery of Kobol by the Colonial fleet (Kobol's Last Gleaming, Part I). These attempts lead to Lieutenant Kara Thrace disobeying orders and taking a captured Cylon Raider to Caprica.
The Arrow was guarded at the museum by a copy of Number Six until collected by Thrace and taken to the Astral Queen and Laura Roslin (Home, Part I).
The Arrow did not in fact open the Tomb of Athena, as stated in the scriptures, but activated a planetarium inside when placed in the bow of the statue of Sagittaron within it. It is not indicated whether the Arrow was recovered from the Tomb after its use.