The clothing serves several purposes, all aimed at promoting and preserving the very rigid, strict ideologies that exist in their society at the time.
The first purpose of the clothing is for indentification and classification. The Handmaids, symbols of fertility and life, are given the bright red clothing. This enables people to identify them immediately, even from a distance, which helps all to show them the "respect" that they are supposed to have, due to their ability to bear children. It also classifies them as a lower-class citizen as far as rights go; no right to a family of their own, they are to belong to whatever upper-class family "owns" them (hence the women having no names, but taking on the name of the man they will bear a child for--Fred turning into "Offred"). The wives wear blue clothing, and are thus allowed other privileges. Other colors classify and divide their society into classes and categories; with the colors and outfits, there was no way anyone was going to strive to rise above their station in life.
The second purpose of the prescribed clothing is to enforce the ideologies and beliefs of the state. The dresses that women wore were all the same, all voluminous and shapeless. This served to eliminate individuality, stifle the expression of one's self through different dress, and to enforce complete and total modesty. No skin was to be seen, no remnants of the promiscuous society. Also enforcing the rules of the society, where women were not allowed to talk to men, and vice-versa, were the restricting head-pieces the women wore. This kept them from seeing anything or anyone or being sneaky in any regard. It also kept the men from seeing their eyes or hair, reducing the chance of personal contact or stimulation. Modesty and virtue were the goals.
What it really comes down to is control. They wanted total and complete control, and these outfits were supposedly helping. I hope that helps; good luck!