A "horn moon" describes a crescent moon that appears U-shaped, with its horns pointing upward towards the sky.
This orientation happens when the crescent moon is positioned in such a way that its arc appears almost perpendicular to the horizon. The visual effect of the horns pointing straight up is most noticeable when the moon is low in the sky. Because the moon's path relative to the horizon varies, this U-shape isn't always visible. Instead, the crescent may appear angled. The horn moon is simply a specific orientation of the crescent moon.