The Alpha Djinn is the original Djinn from which all other Djinns come.
In Season 2's "What Is and What Should Never Be", Dean was kidnapped by the Islamic Djinn, and Dean later killed the Djinn after Sam rescued him. In Season 6's premiere, "Exile On Main St.", Brigitta reveals that the Djinn that Dean ganked was, in fact, the Alpha Djinn, when she tried to kill him. In "Caged Heat", the Alpha Djinn was mentioned by Crowley, when he tried to torture Brigitta into revealing his location.