To hang on, awaiting more news on a subject.
On old dial-tuned AM radios before there were even preset buttons, it was a non-trivial task to tune into a particular station. So radio news announcers would tell their audience to stay tuned to the station if they were expecting more info on the current story."
See also: film at 11
Literally: "(crackle) explosions reported at Pearl Harbor naval base in (crackle) Hawaii...stayed tuned for more news..."
Modern: "Chad's about to tell Rachel he's been cheating on her. Stay tuned for the screaming."