A point is a tie or lace used to fasten a garment and tipped with a chape, tag or aglet. Point, pins and buttons were the most common items sold by Haberdashers and were typically stocked in great quantity. There is even some evidence that Haberdashers were producing and not just re-selling points. By the end of the 16th century, aglets were sometimes used for decoration without the tie or lace and could be ornate, but plain points were also still commonly in use.
Morris quotes from Article 24 in the Book of New Ordinances passed between 1509 and 1635, reproduced in History and Antiquities of the Worshipful Company of Leathersellers of the City of London by William Henry Black 1871: "No person of the said fellowship shall make, or do to be made, any poynctes or laces of ledder, silke, threde, or cadews; but that they shall be well and workmanly made, wrought, and clene sett on, perced and nailed, sharped, fylled and raised." This along with analysis of the insides of surviving aglets, shows that ties were made of leather, woven or braided silk, or wool tape (also known as cadews, caddis or caddow). Aglets varied a little in length and were generally conical in shape. Some of the decorative aglets were also tubular (with no taper). The two main methods of attaching the aglet to the tie are crimping and riveting, though riveting was more common.
Arnold mentions a purchase of tools for attaching the lace to aglet from 1579, "… for a bodkin a Hammer a litell Sythye and other Tooles to tagged Poyntes withal clenlye wrought". This and the ordinance above provide a glimpse of how points and aglets were made. A bodkin was a tool for piercing a hole in textiles and would have been used to make room for a rivet. I have been unable to find what a sythye is, other than possibly a small knife.
There are plenty of examples of points and aglets from finds and contemporary portraits. Each of the points presented here is an example of a type found in period. From left to right:
The Cheat with the Ace of Diamonds, c.1630 - Check out the 'tuft' on the end of the aglets.
Margaret Audley, duchess of Norfolk, 1562 - Decorative aglets on the gown.
The leather jerkin from the Waterer collection in Abingdon Museum has it's original silk points with rivited aglets.