The Ham operator you were listening to was more than likely using one of the many modern radios that allow you to visually 'see' the radio spectrum around the signal they were receiving.
Here's a typical example from the Icom IC-7300 :-
With this functionality they can see a whole chunk of the RF spectrum and the signals within them.
These are often called 'waterfall displays' due to the way the visual data scrolls downwards akin to an actual waterfall.
You can look up videos on their operation by searching for such radios as the "Icom IC-7300" or the "Yaesu FT991a" etc. etc. to see how they operate.
There are ways of performing this functionality on a radio not equipped with such 'delights' by hooking up a SDR or Software Defined Receiver and then using an automatic transmit/receive switch box. That way you transmit on one radio whilst receiving on the SDR via a computer, software and VDU or monitor to view the received information.
A further way is with an IF (Intermediate Frequency) tap where the SDR is directly wired to the receiver circuitry in your radio/rig/transceiver so that the information you see is actually what your rig is receiving rather than just simply the SDR itself.
I suppose there are ways of hooking up standalone SDR units (such as the Malachite?) again using a transmit/receive box mentioned already.
You could for free experience such operational receiving examples with online SDR sites that stream such data across the internet by looking at receivers on the following link :-
Just scroll into the world map where you like and click on one of the many map points to select their receiver....you'll soon be greeted with a reception window and a scrolling waterfall of received signals.
Nowadays as many radios come equipped with such 'features' especially on the Amateur Radio market some people don't seem to be able to live without them. It certainly must look instantly gratifying to see such technology operating and become to rely on it.
Me....I use one of the many radios that don't come equipped with such 'frivolities' <ahem> 'features' instead spinning that VFO or channel selector and simply using my ears to listen instead.
Besides, Panadapters and such aren't exactly a new idea being available for many a decade even in valve guise :-
In this day and age of microcomputers, microchips and pretty colour displays they're infinitely cheaper and easier to bung inside modern radios.
Others will more than likely have various input into this all Thomas probably loving such technology and 'what it can do' for them. So long as everyone is enjoying their radio pursuits who am I to argue.
(I use 'waterfalls' myself for my digimode FT4/8 adventures via WSJT-X so I'm a bit of a hypocrite really.
I hope that helps.
All the best,