The phrase "letting your hair down" means to relax, behave informally, or be at ease, especially after behaving in a restrained or formal manner. The phrase is believed to originate from the practices of medieval and early modern European women. 

During the day, especially in public or formal settings, women would wear their hair up, often in elaborate styles that involved pins, combs, and other accessories. This was a sign of propriety and social status. 

At the end of the day, in the privacy of their homes, women would take down their hair to relax and prepare for bed. This act of letting their hair down was associated with a shift from public formality to private comfort.