The tzitzit are the fringes knotted at the corners of a four-cornered garment, and the tradition is precise that the commandment rests on them rather than on the garment they hang from.
A commandment on the fringes
Numbers and Deuteronomy command the fringes at the corners of the garment, and the third paragraph of the Shema, recited twice daily, states their purpose: to be seen and to bring the commandments to mind. Each fringe is made of threads passed through a corner and knotted in a fixed pattern of windings and double knots, and the numerical values read from the windings are traditionally connected to the divine name and to the number of the commandments, so that the knotting itself is held to encode the thing it recalls.
The blue that was lost and sought again
The Torah specifies one thread of tekhelet, a blue dye, among the white, but the identity of the dye source was lost in late antiquity and the fringes were worn all white for many centuries. Modern attempts to identify the mollusc yielding tekhelet have led some communities to restore the blue thread while others, holding the identification uncertain, retain the all-white fringe, so a single commandment is now observed in two visibly different forms. The making of valid tzitzit is exacting, and a garment whose fringes are torn or invalid is treated as no longer fulfilling the commandment until they are repaired.