What is the plastic tip of a shoelace called?

Answer

It stops the lace from fraying.

Context

The word aglet comes, through Old French, from the Latin acus, meaning needle, the same root behind the word acute. In the 1400s and 1500s an aglet was a metal tag on the end of a lace or cord, used to fasten pieces of clothing together, and sometimes it was ornate jewelry-like decoration. Merriam-Webster defines it today as the tag covering the end of a lace or point.

The purpose is practical. Bare lace fibers fray and flatten, which makes it hard to push the end through an eyelet. A stiff sleeve keeps the fibers bound together and acts like the tip of a needle, letting the lace be threaded quickly. Over the centuries aglets have been made from metal, such as brass, copper, silver, zinc or steel, from bone or horn, and in modern times mostly from plastic that is heated or glued onto the lace, or from crimped metal on some boots and drawstrings.

Historically the idea is older than shoes with eyelets. Laced clothing was common in medieval and Renaissance Europe, where doublets and hose were tied together with laces, and metal-tipped laces made that practical. An aiguillette, a decorative braided cord with tips worn on some military and ceremonial uniforms, comes from the same family of words and uses.

The name is far less known than the object, which is why it often appears in trivia. A shoelace tip has no other widely used English name, and variants such as aiglet and aiguillette are alternative spellings or related terms.