1. To utter loud, prolonged moans. I could hear someone moaning out in the dark, but I couldn't see them. I'll never be able to rid myself of the memory of hearing all those wounded and dying soldiers moaning out on the battlefield.

2. To utter something in a low, guttural, droning voice. In this usage, a noun or pronoun can be used between "moan" and "out." He managed to moan out his name before losing consciousness from the blood loss. It's incredibly awkward hearing to the woman next door moaning her lover's name out in the middle of the night.