Everyone does the hobby differently, but for me I like to listen to folks talking to each other. You could have a guy in Nebraska chatting it up with someone in Australia just talking about whatever. I know this doesn't seem as impressive in the age of the internet, but it was essentially an audio version of the internet before the Internet proper existed for the public.

There are also Radio Nets that happen, pretty much just organized gatherings on a repeater for discussion of a specific topic, kind of like a forum. I like to participate in those because it's very structured and orderly and they cover a lot of interesting topics.

There are yet others who like to do a myriad other things, like see how many hams in other countries they can contact in a day, or learn and communicate in CW/Morse code, or go out to the wilderness/parks to establish contact with someone doing the same thing. The more mechanically inclined might build their own rigs, antennas and shacks and test/use those. And since radio is considered vital communications during natural disasters when the power and internet might be out, some operators regularly practice emergency preparedness exercises for search and rescue, and the like.

These are just a few activities that I can think of off the top of my head, there's many, many more. It's quite a varied hobby!