These are various thickness of suture material (0 is the thickest). With the exception of 0 suture material, all sizes have the -0, and when surgeons want a suture they say “give me a two-oh suture”.
What’s up with the -0? I don’t believe in between thicknesses (2-5 for example) exist.
BTW, here is the Ethicon web page. They make lots of suture material.
If it’s anything like measuring the fineness of sanding materials, “2-0” is actually a way of saying “00.” Sanding materials are measured by grit, and the finest of them are measured as “00,” “000,” and “0000.” There are probably finer grits, but that’s the finest I’ve ever used.
It sounds like the measure for buckshot or fish hooks. The 0 is pronounced “awt” and , I think, spelled “ought”. as in “thirty ought-6”
Anyone know why 0 is called “ought”?
a friend is an artist. For his birthday he told his father he wanted a 3-camel hair brush. Of course he wanted a size three brush made from camel hair. Of course his father looked for a brush made from 3 camel hairs. 
I read somewhere (can’t find it though) that it was a corruption of “a naught” -> “an aught”.
Also mentioned was “a napron” -> “an apron”.
(supported by Merriam-Webster
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Steel wool is designated by using 0 through 0000, and perhaps finer. Abrasive sheets, sand paper, are designated by grit size. Commonly workshop sizes running from 80 to 400 or so. Grits of 1200 or so are not uncommon, with much finer grits available.
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Of course, you’re right, GaryM. I used to build plastic models and would occasionally (before I discovered wet-dry sandpaper) use steel wool for sanding when a very fine “grit” was required. Thanks for the fine-tuning on my reply.
FWIW, I suspect the logic behind the measurement is the same, as I suspect it is the individual fibers (perhaps their diameter?) in steel wool that are actually being measured.
Steel wool? Buck shot? Fish hooks? Sandpaper?
Buck shot and fish hooks I understand. If you get shot or hooked, you need plenty of sutures. Sandpaper and steel wool, though, WTF?!?
We’re talking sutures here people. Not buck shot, not fish hooks, not sandpaper, not steel wool and NOT Byzantine history (50 bonus points if you get the reference). It doesn’t matter how much an 18 penny nail costs (but while we’re on the subject, could someone enlighten me:)).
Actually, it appears the size range is somewhat greater than this. Sizes seem to range from about 8 (the highest size I’ve been able to find; this site mentions a size 8 silk suture) down to 12-0. In general, the larger the number, the larger the size. Until one gets to “0”, anyway. After the “0” size, the “-0” is appended, and larger numbers begin to mean smaller sizes (so, a 12-0 is the smallest suture used, typically for microsurgery). Incidently, the ETHICON site you linked to confirms KneadToKnow’s supposition that a “2-0”, for example, actually represents a “00”:
In the U.S., the system used for suture sizes is from the United States Pharmacopoeia (U.S.P.), and the size is assigned based on “diameter, tensile strength and knot security.” (see here for more discussion).