wet, moist, humid, damp, an illness
濕 centers on the state of being saturated with liquid: wet, moist, humid, or damp. The illness sense is a specific application where dampness is seen as a cause of disease.
濕 combines the water radical 氵 with 㬎, which likely contributes both sound and the idea of moisture. The exact historical development of 㬎 is uncertain, but the character consistently relates to wetness.
Water 氵 on the left and a complex right side 㬎 that looks like threads 幺 being dried under the sun 日 over a fire 灬 — but the water keeps everything wet and damp.
For シツ, imagine a wet sheet hanging in a humid room: sheet -> シツ, and the dampness never dries.