Tznius is a countermeasure to the attempts of the yetzer horah. This explains why, subsequent to the sin of Adam and Chava, mankind suddenly felt a need to be clothed. [1. Bereishis 3:7] Similarly, it is stated in the Gemara [2. Eruvin 100b] that the mitzvah of כיסוי שערות, the obligation for married women to cover their hair — and the obligation of tznius in general — were given in direct response to the sin of Adam and Chava. The deeper meaning of this is that, as a consequence of the first sin committed by mankind, the yetzer horah, which had previously been man’s external enemy, now became an internal foe, interwoven into his emotions and feelings. With this, the passion for sin became far more formidable than it had previously been. To help withstand and overcome this greatly strenghtened yetzer horah, Hashem gave mankind an urge to be clothed and practice tznius in both dress and conduct.
Women in particular, who do not have the mitzvah of learning Torah, were given the special mitzvah of covering their hair in public — a mitzvah which symbolizes the tznius of the Jewish woman. This constant religous mode of dress, and the tznius it represents, becomes a power-pack which gives women a firm attachment to kedusha and emes (sanctity and truth) — which in turn enables them to unmask and expel the yetzer horah before he has chance to do harm.