To send a text message to someone with a lame explanation of why you can't attend your rendez-vous/ party / hang-out / drinks. (Usually a lie.) The main purpose of the texplanation is to avoid the awkward phone conversation where the person to which you are talking totally knows you're lying and doesn't want to accuse you.
Jenny: Ugh, I don't feel like going to Brooke's graduation get together with her family. Her mom's boobs are awful and hard and it hurts when she hugs me. I have to send that bitch a texplanation.
*Whips out cellphone*
Text message: "Hey Brooke! Sory i cant come 2 ur party! my cat is ded and im jst 2 sad!"
Thank God I could texplain my way out of that!