An aglet according to the AHD is

1. A tag or sheath, as of plastic, on the end of a lace, cord, or ribbon to facilitate its passing through eyelet holes.
2. A similar device used for an ornament.

The OED s.v. aglet offers:

a. A tag attached to the end of a lace, originally of metal and now also of plastic, intended primarily to make it easier to thread through the eyelet holes, but also developed as an ornament.

The aglet is that small plastic sleeve on the end of your shoelace. Sometimes aglet refers to ornaments at the end of a lace, especially on shirts or other items of clothing. You see this use in the N-Town mystery cycle play # 26 when the Devil describes the clothing he will offer followers:

Hosyn enclosyd of the most costyous cloth of crenseyn; Thus a bey to a jentylman to make comparycyon, With two doseyn poyntys of cheverelle, the aglottys of sylver feyn (Play 26, Conspiracy; Entry into Jerusalemll. 70–72)

The hose have two dozen points, with fine silver aglets at their ends, serving both to protect the ends of the leather points, and as an ornament. (I’ll take a look at points in the next post.) Etymologically, Modern English aglet descends from Middle English, via Anglo-Norman and Old French aguillette, diminutive of aguille, needle, from Vulgar Latin *acūcula, from Late Latin acucula, diminutive of Latin acus, needle. The same Indo-European root *ak- gives us not only Latin acus, but includes acute, vinegar, acid, and edge, among other words.