I always understood it to mean talking a lot. For example, my friend Crystal can talk for hours and usually "chews my ear off" with all her chatter.

Other opinions may vary.

"Let us remember that there is a creative force in this universe, working to pull down the gigantic mountains of evil, a power that is able to make a way out of no way and trasform dark yesterdays into bright tomorrows. Let us realize the arc of the moral universe is long, but it bends toward justice."
-- Martin Luther King Jr.