The tallit katan exists to solve a practical problem created by a change in ordinary clothing, and it is the garment that makes the commandment of the fringes a constant rather than an occasional observance.
Why it exists
The commandment attaches the fringes, the tzitzit, to a four-cornered garment, and in antiquity ordinary outer clothing had four corners, so the obligation was met simply by dressing. Once everyday clothing ceased to be four-cornered the fringes would have been worn only with the prayer shawl at morning prayer. The tallit katan, a small four-cornered garment worn under the shirt through the whole day, was adopted so that a man carries the fringes on his body continuously, which is the more stringent fulfilment favoured in observant practice.
Worn and shown
The garment itself is plain, a rectangular cloth with an opening for the head and fringes at its four corners, and practice varies as to whether the fringes are tucked in or left visible over the trousers, a difference that in some communities signals affiliation. It is put on with a blessing, and boys begin to wear it young. Where the prayer shawl marks the times of prayer, the tallit katan marks the whole waking day, and the distinction between the two garments is exactly the distinction between an occasional and a constant observance.