A 325 screen has 325 wires-per-inch (the finer of the two screen closeups shown here). Those are grains of salt on it (45 micron openings, a typical human hair is 60 microns wide). A 40 mesh screen is much coarser, it has 425 micron openings (that is a particle of quartz trapped in an opening). A minus 45 mesh powder will be too fluffy to drop through a 325 screen. But particles smaller than 45 microns in a slurry will pass. To get a slurry through a screen this fine one needs to take special measures. I needs to have a high water content so it is fluid. Using a soft brush definitely helps. And a source of vibration. And it is necessary to clean the screen often to remove trapped oversize material. 325 mesh screen fabric is fragile and a sieve like this needs to be treated with care. These cost hundreds of dollars.
The coarsest screen at the top has an opening of 425 microns (that means that 425 micron and finer particles will pass through it, and, conversely, plus 425 micron particles will not pass). It's opening has an area of 180,000 square microns (425x425). Going downward, the openings on each screen have areas half that of the one above. Thus, for the second screen down, the opening area is 90,000 microns. Standardized sieves like this are essential to the study, classification and maintenance of powdered materials. In Insight-live the SIEV test uses this series of sieves.
Sieves are important in ceramics for removing particulates and agglomerates from glaze, engobe and body slurries.