a word occasionally used by old people/ clueless people. What they actually mean is 'Texting' - ie to send a text message.
Or, occasionally used as a term for 'chatting' on-line.
Out of touch with reality person:
"Oh, i can't be doing with all these young people teletexting all the time. Why can't they just pick up the phone and have a conversation like we used to in the good old days."