The tichel is a headscarf tied over the hair by married Orthodox Jewish women, and it is best understood as one of two competing solutions to a single religious requirement.
Covering the hair
The obligation on a married woman to cover her hair is longstanding in Jewish law and is treated by most Orthodox authorities as binding, though its exact scope is debated. Two coverings answer it: the wig, or sheitel, favoured in much of the Ashkenazi and Hasidic world, and the cloth headscarf, the tichel, preferred by most Sephardi communities and by many Hasidic ones, with the choice between them itself a marker of community and custom. The tichel leaves it plain that the hair is covered rather than replaced, which is the ground on which its advocates prefer it.
Craft and meaning
Tying styles are elaborate and regionally distinctive, and the manner of the tying, the fabric and the addition of a shaped pad beneath can signal a woman community and observance to those who read such things. The covering is understood as an expression of modesty and of the married state, uncovered hair being reserved for the husband, and like the other coverings of hair in the tradition it is worn by choice within a framework of obligation that the different communities interpret with real variation.