A metal or plastic tube fixed round each end of a shoelace.The plastic things on the end of shoelaces are called aglets....
And that the ends of our shoelaces are called aglets.
A random search by CFO magazine recently uncovered E-tail sites hawking pipe cleaners, arugula seeds, and aglets (those little plastic things on the ends of shoelaces).
Origin
Late Middle English: from French aiguillette 'small needle', diminutive of aiguille(see aiguille).