This deep stemless cup would have been used for drinking wine. This type of drinking cup with two handles near the rim is also known as a glaux, the Greek word for owl, because of its decoration of an owl between olive branches.
The olive branch appears in the myths about early Athens. Athena won a contest with the god Poseidon about who could provide the best gift to the city. Poseidon brought a spring of salt water to the Acropolis, but Athena brought civilisation by gifting to the city what became its staple crop, the olive.