Post-haste, sometimes written as post haste or even posthaste, is a old fashioned term meaning 'as fast as possible'.
Post-haste is a shortening of the term haste, post, haste, used in the 1500s to mark urgent letters. The 'post' was a courier on horseback who delivered along a given route, and haste meant quickly. These days it might be more proper to write "Quickly, mailman, quickly!" on your letters.
Be that as it may, we usually don't use post-haste to refer to the mail anymore. We use it when telling someone to do something immediately. "Kill those witnesses post-haste!".