This is the term used to describe the number of threads per inch. European measurement is threads per cm. The printer needs to select the proper mesh for the individual job. Fabric printers might use 80 or 110 for applications where they need to lay down light coloured inks on dark fabrics. As the mesh count rises, the amount of ink flow and deposit decreases.
Some inks have specific characteristics which put limitations on mesh counts.
UV inks require thin ink deposits for proper curing, and won't dry in the screen, so mesh counts above 305 are used. Ceramics printing require the coarse particles of glass frit which make up the ink to pass through the mesh openings, so meshes in the 225-250 range are used. Most manufacturers and suppliers can recommend a specific mesh count that works best with their products. A tight screen allows the use of less off-contact when printing, which results in better registration, less distortion, and a sharper print. In many cases it actually takes less pressure to print through a tightly stretched screen then a loose one.