The metric count is based on the number of 1000metres in a kilo of yarn. It's shown as for example, 200/1 NM (new metric) or 120/2, 60/2, 30/3, 14/2, or whatever... so the bigger the "big" number the finer the yarn as you get more metres out of a kilo. The second numbers show how many threads the yarn is made up of. This obviously means you have less meterage as you have two threads. So a 200s yarn is very fine and a 60s yarn is fine but a 10s yarn is significantly thicker.
My weaving silks are maybe 60/2 mainly but my weaving Merino (for scarves) is currently a 14/2.
There are numerous systems and they are all still in use to a greater or lesser extent. Different places developed different systems - Yorkshire had it's own wool count for example and I have some old cones labels in YWC !