睡 is anatomy in two parts: an eye 目 beside 垂 (to droop, hang down). Drooping eyes — sleep, written exactly as it feels at 11 pm over your homework.
睡 pairs with 觉 in 睡觉 (to sleep), the verb every learner needs by day two. 午睡, the noon nap, is a protected institution — Chinese schools and offices dim lights after lunch, and 睡懒觉 (sleeping in) is the weekend's sacred right. The character is honest: no metaphor, just eyelids giving up.
Eyes 目 drooping 垂 — SLEEP.
午睡 (the after-lunch nap) is written into many Chinese school schedules — desks double as pillows nationwide.