What does it mean if you keep having dreams about a TV show?
Well, this is rather broad. But let me give you some things to think about.
(1) You need to explore your connection to the show. Is it one of your favorites? One you watch regularly? An old one no longer on the air? One from your childhood? Did you watch it with family and/or friends? Have you been binge watching it?
If it's something you've been watching a lot of, or a show you think and talk about regularly, it may mean nothing to dream about it. Your subconscious may simply be emptying its trash bin.
If it's a show you watched as a child, something you have a nostalgic connection to, then there may be something in your past that is affecting your present and your subconscious is trying to point you in that direction.
(2) What's actually on the screen? The characters, the actors, the dialogue, the situation itself all contributes to the overall meaning of the dream. Are you one of the characters? Or are you just watching the show? If you're one of the characters, think about ways in which you are similar to him or her. Why are you that character? How does that role reflect your living "role" in the waking world?
Of course, it could be nothing more than romantic fantasy. Sometimes you might be yourself in the dream, interacting with favorite characters. If you have a crush on one of these characters/actors, then your subconscious may just be playing around.
As for the situation in the show/scene: Is it scary? Funny? Romantic? Is it a chase scene? How do you feel about it? If you're in the show, are you frightened? If you're just watching, are you tense? Uncomfortable at watching two people kiss?
(3) Active vs Passive. Watching a TV show in a dream is different than being a part of the show. I've touched on this a little bit above. In a lot of dreams, screens (TV, movie) symbolize a story—often the dreamer's life story, or a portion of it. If you are merely watching the show or movie, it could mean you're letting your life go by. If you're actively participating, then you need to look at whether you're playing/pretending (being insincere in real life), or if you're being true to yourself.
(4) Finally, is the dream recurring and mostly the same, or are you dreaming about this TV show but in a lot of different ways? A recurring dream is often a sign your subconscious wants you to pay attention to something very specific. Or it may be that your subconscious keeps coming back to this particular scenario because it is trying to work something out, put together a puzzle.
But if you're dreaming about the same show but the dreams are all different . . . Is there any common thread besides the show? Are you always the same character, is the location the same each time? If not, it's possible once again that your mind is simply dumping a lot of subconscious waste matter. But if there's something about these dreams that seems to connect them, that would be the place to start.