“Let your hair down” means “to relax and do what you want”.

Example: It’s been such a hard week at work. Should we all go out tonight and let our hair down a bit?

Origin: This phrase originated in the 17th century, when women were expected to wear their hair up in public, either in a bun, pinned on their head or in elaborate styles. The only time they could let their hair down was for washing or brushing, or when they were alone at home and could relax.