The little plastic tip at the end of your shoelace is called an aglet. If the aglets wear off, it can be hard to lace up your old basketball sneakers.
There are two ways to spell this very specific thing, the plastic or metal shoelace tip that makes it fit more easily through the eyelets in your shoes: aglet and aiglet. Sometimes the aglet makes your life easier, and in other cases it's just for decoration. The Middle French root is aiguillette, a diminutive of aiguille, "needle," from the Latin acus, which also means "needle," by way of its own diminutive, the Late Latin acucula.