Flat braid(ed) wicks are used mainly with pillar and taper candles (taper candles are those long, thin candles obtained by dipping a wick several times in melted paraffin to build up layers of wax).
Flat braid wicks are made of 3 braided bundles of threads, each bundle being made of a certain number - small or large - of threads (also called ply). It is braided in such a manner that all three bundles lie flat and is referred to by the number of plaits it contains.
The wick is referred to by the total number of ply it is made of. Thus, the larger the number, the thicker the wick will be.
Because the number of braided bundles is always 3, the number of threads will always be a multiple of 3.
Candlewic, a US manufacturer of candle wicks, offers the following wick sizes in the flat braid range: 12 ply (the thinnest), 15, 18, 21, 24, 27, 30, 36, 45 and 60 ply (the thickest, used in pillar candles with a diameter between 12 and 15 cm).
One of the advantages of a flat braid is that it will curl slightly while it burns, preventing the formation of carbon on the wick (an annoying phenomenon called mushrooming) and makes it almost self-trimming (because the wick curls, its extremity ends up in the hottest part of the flame where it will eventually carbonize. Because of this, the wick must be trimmed less often than it used to before flat braid wick was invented).
It is possible that your wick supplier doesn't use the number of ply to identify flat braid wicks but rather indicates the size and type of candles they are most appropriate for.