A period of excessive or uncontrolled texting between two or more people, usually associated with meeting a new prospective partner with whom you just can't stop talking to. After binge texting, facebook-officalness ensues.
After Jane and Alex talked for 12 straight hours through text messaging,
Jane: Have you ever heard of binge texting? I think we just partook...
Alex: Hey accept that relationship request i sent you on facebook!