This is a frequent question found at quiz nights and on crosswords. The answer is an AGLET.
Aglets are metal or plastic and ensure that the fabric of the shoelace does not fray and unravel.
According to Wikipedia, wealthy Romans would wear aglets made of brass or silver.
In James Cave's article; "Behold the Aglet, that thing on the end of your shoelace" James describes the aglet as the most useful invention you've probably never thought about. Of course, James wasn't talking to me, as I think about aglets all the time!! :-).
In addition to ensuring your shoelace doesn't unravel, the aglets other role is to make lacing up shoes a much easier task. Can you imagine having to lace up your shoes without the sturdy guidance of the metal of plastic tip?
Here at Cute Laces HQ we add metal aglets to the ends of our Cute Laces, just like the Romans!