Why do CIA and other spy types touch their ears in movies? And do people really do that?

In a loud environment you can make a badly fitting earphone clearer by pushing it in to create a better seal and block outside noise.

I’m not a spy but I have the same trouble with my earpiece which keeps falling out when I’m listening to music. To hear properly I have to press the earpiece to my ear. In movies it isn’t necessary but may have evolved as a theatrical gesture to make clear to the audience what is happening.

Back in the day, stone age, the ear pieces had PTT, push to talk controls on the ear piece. When pushed it enabled the mic and turned on the transmitting stage. This saved battery power and reduced the chance of other people talking over each other.
Later they moved to VOX meaning voice activated switch.It would turn on the the transmitter if it heard your voice. It was hands free. But that caused problems by missing the beginning of messaged and unintentionally activating when other people nearby were speaking.
Over the past 25 years many improvements have been made: voice recognition, digital ID, GPS, transmitting power levels, noise cancellation, internal accelerometers. increased battery life. Think of Apple AirPods on steroids. 25 years ago that was a fantasy.

Common for many reasons. Better fit due to movement, human nature to try to head better, touch activation to change from noise canceling to hear thru, touch action to enable mic function, itchy ear from sweat buildup wearing an earpiece for long durations, former baseball player.

I was never a spy, but I had to wear earpieces in executive, and private security jobs. Most of the above is true. One thing I would add is, to conceal what’s being said to you whilst talking to a person of interest. People with good hearing can hear an earpiece, on another person. If they hear “he’s got a warrant,” they might take off or pull a weapon on you.

Earpieces are nice, but they have drawbacks. If you have to get physical with someone, they’re a problem. I got hit in my left ear often when things went sideways. If I had an earpiece in, it was a really shitty experience.

A book on body language would probably explain it.
I would say it signals the speaker’s inability to answer the question or comment at that exact time, it taking some thought. (This assumes there is no electronic device.)
With some device, it might signal the user’s intension to concentrate on what was being said through the device.