An aglet is a small plastic or metal sheath typically used on each end of a shoelace, cord

Rope

A rope is a length of fibres, twisted or braided together to improve strength for pulling and connecting. It has tensile strength but is too flexible to provide compressive strength...

, or drawstring

Drawstring

A drawstring is a string, cord, or rope used to "draw" or tie closed an opening in fabric or other material...

. An aglet keeps the fibers of the lace or cord from unraveling; its firmness and narrow profile make it easier to hold and easier to feed through the eyelets

Grommet

thumb|right|250px|Some rubber grommets.A grommet is a ring inserted into a hole through thin material, such as fabric. Grommets are generally flared or collared on each side to keep them in place, and are often made of metal, plastic, or rubber. They may be used to prevent tearing or abrasion of...

, lugs, or other lacing guides.
The word aglet (or aiglet) comes from Old French

Old French

Old French was the Romance dialect continuum spoken in territories that span roughly the northern half of modern France and parts of modern Belgium and Switzerland from the 9th century to the 14th century...

 aguillette (or aiguillette), which is the diminutive of aguille (or aiguille), meaning needle.