A screen either passes ink or blocks it, so on its own it can only print solid shapes. Halftones break a tone into dots: large, close dots read as dark, small, scattered dots read as light. From arm's length the eye blends them into a smooth gradient, a shadow or a photo.
Dot frequency is measured in lines per inch (LPI). Garment printing uses much coarser halftones than paper printing, because fabric is textured and ink spreads a little. The printer matches the LPI to the mesh count so the dots do not fall through the gaps between threads. The very lightest dots can vanish and the darkest can merge, so those ends of the tonal range need care.
Halftones power simulated process and four-color process prints, and they let a one-color design suggest depth. If your art has soft shading, ask how it will be separated and request a close-up proof. See separation methods compared.