The Gold Key is a simple golden key that Kratos takes from the purse of a woman in the Athens Town Square who fell from a balcony, to her death, while fleeing from him. Kratos then uses the key to unlock a trap door into a series of tunnels that then lead to the Rooftops of Athens. It is possible that this woman may have been important if she had access to these areas, otherwise, it's not stated how or why she had it.