千 is a person 人 with a tally stroke across the leg — the ancient bookkeepers' way of writing 'one thousand people'. Big numbers were counted in bodies: an army's arithmetic.
千 is Chinese's favorite hyperbole: 千万 (ten million — but as an adverb, 'whatever you do…!': 千万别忘了, absolutely don't forget!), 千里 (a thousand li — every epic journey's unit: 千里之行始于足下, a thousand-li journey starts under your foot). 一日不见如隔三秋 has a cousin in 千言万语 — 'a thousand words, ten thousand sayings' — for when feelings overflow vocabulary.
A person 人 tallied with one stroke — counting by the THOUSAND.
千万 as an adverb means 'by all means / absolutely' — because if you say it ten million times, you mean it.