In classical legend, Cyrene was a nymph and virgin huntress, with similarities to the goddess Artemis. The god Apollo became enamored of her, and by him she had two sons -- Aristaeus and Idimon. When Apollo carried her off, he brought her to Libya where he made her a queen. Today, the city of Cyrene in Libya derives its name from this legend.
Cyrene's son Aristaeus is said to have grown up to become a patron deity of olive plantations and shepherds, and he is said to have instructed mankind in the art of bee-keeping.
Cyrene's son Idimon is said to have been one of the soothsayers who accompanied the Argonauts.
As for the meaning of the name "Cyrene" -- I'll leave that to our resident Greek etymologist, Pavlos. :)