To make or become faster or more rapid; to stimulate or accelerate a process or activity.
From Old English 'cwician' meaning 'to make alive' (from 'cwic' meaning alive or living). The original sense was to give life to something; the meaning of speeding up developed because living things move faster than dead things.
The word 'quick' originally meant 'alive' - hence 'the quick and the dead' in old texts means 'the living and the dead'. When we quicken something, we're metaphorically bringing it to life or making it more lively and active.
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