Ply is related to the layers of substrate such as cotton in the case of rag mat board used to create the mat. 4-Ply is the most common and is approximately 1/16 inch thick. 8-ply will be twice as thick or about 1/8 of an inch. 6-Ply of course will be in between. 2-ply board is only 1/32 of an inch thick and is not really used like a traditional mat board. It is too thin for a meaningful bevel cut in the opening window. 2-Ply is primarily used for archival mounting purposes when you want to mount on cotton rag board. Since the 2-ply is thinner it less expensive, however it is not thick enough to serve as a frame backing so it will need to be backed with something like foamcore.
A lot of mat board is made from other substrates like wood pulp or alpha cellulose and does not appear to actually be composed of individual layers or ply's and the manufactures do not seem to refer to them as 4-ply or 8-ply. They will be standard or double thick where standard is about 1/16 of an inch. For clarification and lack of more common term I choose to still refer to these as 4-ply on my frame companies website.
Different companies 4-ply or 8-ply or standard mat board will be different thicknesses. I have noticed that Bainbridge 8-ply alpharag will be a full 8th of an inch thick and many other companies will be just a little thinner. Also, although the Bainbridge 4-ply alpharag matboard is a full 1/16 inch thick, the Bainbridge alphamat is a little thinner, and the paper matboard that we sell is thinner still.
One of the reasons I really like the Bainbridge 8-ply rag mat board is that because it is a full 1/8 of an inch thick and we cut the bevel at 45 degrees it results in a bevel that is nearly 1/4 of an inch and is therefore visible at typical viewing distances and thereby adds signficant presence to the framing package.