means To make the soft, continuous, low vibrating sound a contented cat produces — or, of a person, to speak in a similarly smooth, pleased, throaty way.

from An imitative word, coined to mimic the very sound it names — what linguists call onomatopoeia. English picked it up only a few centuries ago, and you can hear its kin in other languages doing the same trick: each one reaching for that low rolling rrr the cat makes. No deep root to trace; the cat simply told us what to call it.