The obligation on a married Jewish woman to cover her hair is long established in halakhah, and its usual textual anchor is the ordeal of the suspected wife in Numbers 5, where the priest uncovers or loosens the woman's hair, from which the Talmud infers that covered hair was the normal state. Rabbinic discussion distinguishes what is required by the law of Moses from what is required by the custom of Jewish women, and the covering falls partly in the second category, which is why practice varies so widely by community while the principle does not.
The tichel, called a mitpachat in Hebrew, is the scarf answer to that requirement, and it is the preferred form in most Sephardi communities and in many Hasidic ones, in preference to a wig. Other forms exist within the same communities: the snood, a knitted or fabric bag; the hat worn over a partial covering; and among some Hasidic groups the shpitzel, a partial hairpiece worn with a headpiece.
What a woman wears is usually legible to those who know how to read it, indicating not only that she is married but which rabbinic authorities her community follows and how strictly. Some communities require that no natural hair show at all; others accept a handbreadth.
The tying itself has become a genuine craft with a contemporary following. Multi scarf wraps using two or three fabrics, volumising pads underneath, regional knots and a large body of instructional material circulate widely, and there are designers and shops serving it. That is a reminder worth keeping: a covering adopted in obedience to a rule is not thereby experienced as plain, and the women wearing them are frequently the ones who made the style.