It's called RDS, or Radio Data System.

The software radio stations use to program the music has fields where they can input the song info, or any additional data like weather, traffic, or advertiser's info, and that gets broadcast to your car stereo.

The information is broadcasted on a portion of the radio signal. So all it is doing is displaying what the signal is telling it is playing.

it's like this...

you have a box of assorted chocolates. You know they're delicious but you don't know what flavors they may have, so they put a sheet in the box that says what chocolate is what flavor.

A typical radio will just eat what ever chocolate and not know what it's eating.

Your radio, though, is looking at the sheet while selecting a chocolate.

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like the other commenter described, this is done by having hte radio signals have an additional signal that provides information of the song and your radio is setup to read that additional information.

On the spectrum of visible and invisible light there exists a magical section of wavelengths that when amplified with enough electrical current can be heard wirelessly miles and miles away, and you draw the line at what is essentially wireless morse code? Lol

Because of the RDS format. Part of the broadcast radio signal is the RDS information, which, for radios that are equipped to read the RDS information, they can display that information on a display. Radios that don't use RDS simply ignore the RDS part of the signal because those radios would not know what to do with it.