The phrase “let your hair down” is an idiom that means to relax or let go of inhibitions. Most language experts agree that the idiom is from the time period when it was only proper for women to wear their hair pinned up on the head in public. They were only allowed to let their hair down to hang naturally when alone, either when bathing or at bedtime. Letting one's hair down, at that time, was reserved for moments when relaxing and behaving less properly were acceptable.
Most of the time, the idiom is not intended to mean “relaxing” as in calming, soothing, or otherwise stress-relieving situations such as quietly sitting to read a book or getting a massage. Instead, it more accurately refers to relaxing social rules and letting go of inhibitions that would normally hold a person's behavior in check. For example, it would be a correct use of the idiom to say that, halfway through a party, you let your hair down and danced for a few songs, when you had been previously too embarrassed to try. It would be incorrect usage of the phrase if you were to let your hair down by slipping into the corner of the room and listen to some calming music in order to relieve anxiety and build your confidence.
Friends may often advise their peers to loosen up and stop worrying so much what other people think. In the example of an anxious individual too afraid to dance at a party, a friend might convince him or her to let go of any inhibitions by saying, “Come on, we are at a great party, let your hair down a little. Everyone else is dancing too and will not notice if you mess up.”
Sometimes, the idiom is somewhat incorrectly used to mean dressing down, or going from formal to informal clothing as opposed to attitudes and social behaviors. An individual might have a routine of coming home from work and letting his or her hair down by changing from business clothes into more comfortable clothing, such as a t-shirt and jeans or sweatpants. It is also possible that, similar to the idiom's origin, you can quite literally let your hair down out of its formal style into a more relaxed, natural and comfortable style. While this is not a technically correct use of the phrase, it is used in this manner often enough that other people will understand the meaning anyway.