残月 refers to the waning moon — the crescent-shaped moon visible in the late night or early morning sky as it shrinks toward the new moon. In classical Chinese poetry and literature, it often carries a melancholic or lonely atmosphere, associated with parting, longing, or the end of something. It's a literary term you'll encounter in poetry and prose, not in everyday conversation about the moon (where you'd use 月亮 or 月牙).