One common type of activity is attempting to make direct contact with a distant station. This could be using a voice mode, digital mode (text), or CW, which just means using Morse code and a keyer to communicate.
Operators can make contacts all over the world using the Earth's ionosphere as a mirror, to reflect signals, and send them further than any method of terrestrial propagation can achieve. This is called skywave propagation as opposed to groundwave propagation, which is like how cell phones work.
The caveat being that skywave propagation appears to have a degree of randomness to it. It isn't totally random but we collectively do not understand it enough to fully predict when and where our signals will end up.
So there's an opportunity to make direct contact with another station somewhere else on Earth, depending on the propagation conditions.
So to now actually answer your question, there's novelty in getting your station working, and then using it to have a brief conversation with a random person at least hundreds and sometimes thousands of miles away. This is known as a QSO.
At different times, for example, with my station being located in North Carolina, I might suddenly be able to reach stations in Europe around sunset. Usually, it's more limited to random areas within the United States with a basic antenna, but not always.
If I announce my presence over the radio (call CQ), and someone comes back to me, we'll exchange some basic signal quality info. Afterwards, if the other person wants, you can ask about their radio setup, and talk about common interests, while avoiding some topics like local politics, etc.
Here's a video of someone doing this: https://youtu.be/tXIbSGX2SvU?t=3m40s
That's only one activity while there are many others. Another activity would be pointing a beam antenna at low earth orbit amateur radio satellites to make as many quick contacts with other operators as possible while the satellite is above the horizon. This is a very physically and mentally challenging activity. Here's a video of that: https://youtu.be/QWtdyT4PYMw
There are also digital modes as well. FT8 is a common digital mode for making contacts with much less personal interaction using a PC. This one is easier to just watch and see than to explain: https://youtu.be/bSpyYV-xz5c
Hopefully that gives you some ideas about what it's like to make contacts over the radio. Some people like the social aspects and others (like me) like the technical and experimental aspects of making contacts and seeing where and how far my signals will go.
The fact that someone made the FT8 modulation scheme up out or the blue and people started adopting it and using it and having fun shows the spirit of ham radio.
I bet there are folk on here who would be able to come up with some interesting new modulation schemes to push the envelope even further.
It's a shame that the venn diagram intersection between the modern tech world and ham radio isn't larger.
Just tune in to 14.074Mhz and listen for the strangely melodic modem-like tones. Download WSJT-X and pipe one into the other.
It was at this point I was annoyed to find my new PC doesn't have a mic socket (what's that all about?), but in fact holding my usb webcam up to the radio's loudspeaker was enough to get reports from all over the continent appearing.
The exam system was figured out by some group in Texas. Their system was approved by the FCC so my local group piggybacked off of the Texas group to do the online exam.
There was a zoom call at a certain time. You had to do certain things to your computer ahead of time to get it ready. When it was time they had me turn the laptop all around to show my room to prove there was no one and nothing other than a plain sheet of paper, a basic calculator, and a pencil nearby. I had to prove the paper was blank and the calculators memory was wiped. I had to have all family members leave the house during the exam. There were five other people on the call all watching me over my camera while I took the test. The proctor took control of my computer to see what I had running and to start the exam. Then I took the exam. I missed one question, but they can’t tell you which one you missed. I really thought I got them all right and it still bothers me not knowing which one I got wrong ;-)
Afterwards the Texas group was given my information and they submitted it to the FCC. I got my license a few weeks later in an email.
I haven't tried online testing yet. I've been putting off upgrading to Amateur Extra class, though I'll probably try one of those online test sessions eventually.
Ham radio is a very interesting hobby with a large variety of activities and operating techniques. It's been great to learn about how to make direct contacts across the world using just a small antenna and coil using the HF bands.
I certainly understand the potential commercial value of spectrum currently allocated to amateurs, though it's a shame to see it constantly under threat, with little regard to its usefulness as an emergency communication service.
While it's true that most amateurs are older, I'm 24 and I would encourage anyone looking for something else to do to get licensed and get on the air. There's always something more to learn and do, and many hams are happy to help with choosing and setting up equipment.
Check out hamstudy.org if you want to get licensed. It's pretty easy, especially to get a basic Technician class license, and online testing has begun due to the COVID-19 pandemic.