When you hear Morse Code being used in movies or TV shows, does what they're doing actually mean anything? Or is it just random clicking?

It depends on the movie or show; mainly how much they're willing to spend on consultants to ensure realism. Sometimes they're just random beeps; sometimes they're genuine Morse that fits in with the script/dialogue; sometimes they're stock recordings of valid Morse that is totally unrelated to the story.

Given the diminishing numbers of viewers with knowledge of Morse then stock recordings tend to be used much more often.

A give-away that fake Morse is being used, is when the operator is just tapping the top of key with their fingers; genuine operators would hold the key in a fist-grip.

Fun Morse Code Fact: The theme tune to "Inspector Morse" spelled out M.O.R.S.E. in Morse code; and the composer often spelled out the name of the murderer for that episode in the incidental music - in later series he'd also spell out another character's name as a red herring. I watched the programme for four years before finding this out - I was convinced my granddad (former RAF radio operator) was some sort of mastermind of criminal detection - turned out he just listened to the music.

It will vary with the movie or show.

Some use real signals; others use gibberish.

If you get a Morse code reader, you can find out...

A friend said they were sending a string of T's in a movie we were watching. He is a radio ham and knows such things.