The tallit is widely treated as the object of the commandment, but in the internal logic of the tradition the shawl is only a means to an end.
The fringes are the point
The commandment is on the fringes, the tzitzit knotted at the four corners, and the shawl exists so that there are four corners to attach them to. This inversion, garment as scaffolding for the fringes, explains why the tallit katan was later invented to keep the fringes on the body all day once ordinary clothing stopped having four corners. Many wearers draw the shawl over the head during particular prayers to enclose themselves, and a person is frequently buried in a tallit with one fringe cut, the cut marking that the obligations no longer apply.
Who wears it, and where it is contested
The tallit is often given at bar or bat mitzvah or by a spouse at marriage. The wearing of it by women is unremarkable in Reform, Reconstructionist and Conservative practice and is not the custom in Orthodoxy, and at the Western Wall it has been the subject of arrests, litigation and the long-running dispute over the Women of the Wall, which makes a prayer shawl one of the sharper flashpoints in contemporary Jewish public life.