Other forms: stayed tuned; staying tuned; stays tuned
When your sibling wants to stay tuned during a TV commercial, they won’t let you change the channel! And if someone invites you to a party without saying where or when, they’ll ask you to stay tuned for more details.
Stay tuned comes from the field of broadcasting. To watch or listen to a radio or TV program, you have to be tuned to the right station, so staying tuned means sticking with that station and waiting for the program to continue. Even with a podcast or online video, there may be interruptions for advertising, and users will be told to "stay tuned for the next segment." From there it’s an easy jump to the idiomatic meaning of waiting to hear more from someone about something.