early 14c., "cessation" (of pain, grief, etc.), from slack (adj.).
The meaning "a cessation of flow in a current or tide" is from 1756; that of "still stretch of a river" is from 1825. The meaning "quiet period, lull, interval in activity," especially in reference to business, is by 1851.
The meaning "loose part or end" (of a rope, sail, etc.), having no stress upon it, is attested from 1794; hence the figurative senses in take up the slack (1930 figuratively) and slang cut (someone) some slack (1968).