The tallit accompanies a life at three points and the same cloth can serve all three.
It is commonly given at bar mitzvah, or in Ashkenazi communities at marriage, and the difference between those customs is itself a marker: most Ashkenazi men traditionally begin wearing a tallit gadol only when they marry, so an unmarried man in the congregation is visibly unmarried, while Sephardi and Yemenite practice has boys wear one from bar mitzvah or earlier. At a wedding the tallit is sometimes held over the couple as the chuppah, or draped over them during the ceremony. And a man is customarily buried in his tallit, with one of the four sets of fringes cut or removed, because the dead are exempt from the commandments and the garment must no longer be fit for its purpose.
The atarah is the decorated band at the neck edge, which serves the practical function of marking which way round the garment goes, and often carries the blessing said on putting it on.
The blue thread is a separate matter. Numbers 15 specifies a cord of tekhelet among the fringes, and for most of Jewish history no tekhelet has been used, because the identity of the creature yielding the dye was lost. Most tallitot accordingly have white fringes with black or blue woven stripes in the cloth, which are decorative and not the commanded thread.
Drawing the tallit over the head to form an enclosure during the Amidah, or at particular moments such as the priestly blessing, is a widespread custom, and under the tallit at Kol Nidrei or during private prayer it functions as the nearest thing Judaism has to an enclosure for solitary prayer in a public room.