Azaroth was a minor goddess of the Calormene Religion. The Calormene religion was a polytheistic one, worshipping many deities: Tash and Zardeenah were two others. In the legendary hierarchy of Calormene deities, Azaroth was considered below Tash (the highest of Calormene deities) but above Zardeenah, the goddess of night and of unmarried maidens. Azaroth commanded more respect and fear than Zardeenah, though her exact position and responsibilities is not clearly known.
C.S. Lewis never defined whether Azaroth was a god, or a goddess. In Paul F. Ford's book, entitled Companion to Narnia, Revised Edition: A Complete Guide to the Magical World of C.S. Lewis' The Chronicles of Narnia, Azaroth is assumed to be female, as here.
Azaroth might be based on the Phoenician goddess Astarte (a variant of the older Mesopotamian Ishtar/Innana), whose worship competed with early Judaism and is the origin of several Abrahamic demons like Astoreth.