It is perhaps supposed to represent the compass of Argo Navis, though the Argo could hardly have had a compass, as the ancient Greeks knew nothing of compasses for navigation. Pyxis was not formerly a part of Argo Navis, thus the stars in it have their own independent Bayer designations (unlike Carina, Puppis and Vela which retained and split among themselves the Bayer designations from Argo).
It should not be confused with the constellation Circinus, which represents the type of compass used by a draftsman or cartographer.
Since it is a modern constellation, it has no independent pre-17th century mythology associated with it.