A woman may not go outside on Shabbat wearing either woolen strands or linen strands, or straps on her head, and she may not immerse herself in a mikveh while wearing them, until she loosens them.
What does mikveh have to do with it? - It actually gives another reason: if a chance to perform a mikveh immersion (such as needed for eating tithe) will present itself, she may take them off, immerse herself, and then forget to tie them back and come to carry in a public area.
Neither may she go out with a "totefet" - an ornamental band going to from one ear to the other, made either of colored strands or of gold or silver. It is called a "totefet" because it is warn in the place of tefillin.
Some say that the prohibition is not only against wearing these items in a public area, but even in one's own courtyard, for she may then forget and step outside. Regardless of the rules above, it was a custom of Jewish women to wear jewelry and ornaments on Shabbat as far back as the tenth century. The reason for it is a subject of much discussion.
Art: Isidor Kaufmann - A Jewish Bride