To stay up all night, texting/talking with another until someone stops making sense because of how sleepy they become.
When two people are owling a lot throughout a course of time, they are termed owl partners
Ghinz: Hey Moudi, we're going to be owling all night tonight!
Moudi: hahaha for sure! Can't wait to screenshot something embarrassing you say!
Ghinz: Lmao you're such a mean owl partner !