Count the number of openings in one inch of screen is the mesh size. So a four mesh screen means there are four little squares across one linear inch of screen. A one-hundred mesh screen has one-hundred openings, and so on.
Now it comes to filters, which may be made of many materials other than wire screen, are rated by micron size. A micron is 1-millionth of a meter or 39-millionths of an inch. For comparison, a grain of salt is about 70 microns across. Red blood cells are 12 microns and the smallest particle visible to the naked eye is about 40 microns.
These screens play an important role in the kitchen and are handy at all times. For clarification of a broth made from katsuobushi and niboshi, it is very handy to strain the broth to get it clear.
But we must be careful not to take out the natural micron ingredients that lend to the flavor and add nutrition of micro particles. Very often in western foods we need to clarify a broth that gets dirty in the process. In the preparation of these broths, such tools are very useful but usually a bag is more suitable.
The copper wire is used to strain tea and the far right I use for different purposes and the middle is super micron with a double wire bag. This will catch almost any micro particle.