Just to jump on miamigrad's very complete answer: There are three OneWorld elite status levels: Ruby, Sapphire, and Emerald. OneWorld alliance members (e.g. AA) also have elite status levels. In the case of AA, they are Gold, Platinum, and Executive Platinum.

As per AA's agreement with OneWorld, AA's elite members also enjoy one of the three levels of status levels with OneWorld.

AA Gold is also OW Ruby.
AA Plat is also OW Sapphire.
AA EXP is also OW Emerald.

If you have OneWorld status (by earning status on one of the member airlines), you enjoy the privileges of OneWorld status on any member airline.