There is an old tradition in two-way radio communication of saying “over” to indicate that the speaker is through talking and inviting the other person to speak. You are turning the air over to the person you’re speaking with. When you’re done speaking, you terminate the conversation by saying “out.”
For some reason, Hollywood and radio scriptwriters thought it was neat to conclude radio conversations with “over and out,” but this would technically mean “You can talk now if you want, but I’m not going to be listening.”
Today “over and out” lives on mostly as an ill-remembered allusion to those old movies and shows in song lyrics and punning headlines. Radio communication buffs, however, cringe when they hear it.