Meter is a very ancient musical element and extends back into human prehistory. Ancient poets may have borrowed the idea for metered poetry from musical meter. Say the words of your favorite pop song in rhythm and you will sense poetic meter as well as musical meter.
Musical meter seems to have originated with the perception of the human heartbeat.
Ancient songs were metered as well as the texts of ancient plays. Meter is a metaphor for all the periodic aspects of the human life experience. Measures of music have a periodic aspect to them in that they are repeated one after the other.