The basic feeling of being unhappy, down, or low..
The broad, neutral base term for unhappy feeling — usable for anything from a small letdown to a great loss.
A general term usually without implications about the cause or intensity of unhappy feeling — the widest in scope and the lowest in commitment. Sorrow is deeper and tied to loss or regret; grief is acute and usually from bereavement; anguish is agonizing; melancholy adds a reflective, pensive coloring; gloom suggests a dispiriting atmosphere; dejection is a more temporary downcast low; despair adds loss of hope. Plain and everyday, usable in any context.
The noun is Middle English sadnesse “seriousness, firmness,” from sad + -ness. The adjective sad is Old English sæd “sated, full, weary,” from PIE *sa- “to satisfy.”
A notable arc: sad shifted from “sated / full” through “heavy, weighed down” to “weary,” reaching “unhappy, sorrowful” by c. 1300; earlier senses (“firm, sober, serious”) are now obsolete, and sadness itself once meant “seriousness.” No reliable recent-generation shift to the core meaning.