It begins with a capital letter and ends with a period. It IS a complete thought and can stand alone. It only forms part of an idea and is only part of a sentence. While the playful kitten danced the Watusi. Since they had locked the keys inside.
Some fragments have verbs, but their subjects are missing.
By dancing and singing all night. By dancing and singing all night is a fragment without a subject. The white mice celebrated by dancing and singing all night. They were dancing and singing all night. Many people use coupons.