This was one of the first unusual words I learned. I read about this somewhere when I was a child and it opened my eyes to the fact that English has a word for just about everything. I had no idea prior to this that there was a particular name for the ends of one's shoelaces.
1. The metal tag of a lace (formerly called point), intended primarily to make it easier to thread through the eyelet-holes, but afterwards also as an ornament to the pendent ends.
2. Hence, An ornament consisting a. properly, of a gold or silver tag or pendent attached to a fringe; whence b. extended to any metallic stud, plate, or spangle worn on the dress.
c. esp. A tagged point, braid, or cord, hanging from the shoulder upon the breast in some military and naval uniforms. In this sense now officially treated as Fr., and written aiguillette.
3. ‘Still used in haberdashery, and denotes round white stay-laces.’ Drapers' Dictionary 1882.
[So in mod.Fr. aiguillette has passed from the tag to the lace or cord, as point did in Eng.]
4. Herb. Any pendent part of a flower resembling the prec., esp. a. A catkin of hazel, birch, etc. b. An anther (only in Dicts., and perh. erroneous).
5. A fragment of flesh hanging by the skin. Hence, a scrap, a shred. (Cf. Fr. découper un canard par aiguillettes, Littré.) Obs.
6. Comb. aglet-babie, ? A doll or (grown-up) ‘baby’ decked with aglets. (Explained by some as an aglet shaped like a human figure. Johnson defines aglet as ‘A tag of a point curved into some representation of an animal, generally of a man,’ but no quotations have been found bearing out this statement, which was perhaps merely hazarded as an explanation of aglet-babie); aglet-headed, having a head resembling an aglet; aglet-hole, a hole for passing a lace through, an eyelet-hole.