Jothar, years ago it was a way to speak to people all around the world with a station located in your house and a special antenna on the roof. After you bought or built the equipment, you could use it as much as you want and there were no further charges, since you are directly transmitting via short wave (which can go long distances) to the other station. You are not using any provider like a cellular company or an ISP.
Because your signal can be powerful (up to 1,000 watts) which is much more than a CB radio (limited to 5 watts), there is a remote potential to harm oneself with the high voltage equipment, and also a possibility to interfere with other urgent communications, like aircraft, police, or even TV and radio. Therefore the FCC requires you to pass a test on electronic theory and rules and regulations and also on Morse Code, since the first radios were built by hams and this was in the day of telegraphs, so they wanted to keep the tradition alive.
Typically one can either arrange to speak to someone on a specific frequency at a specific time, or one can put out a general call to speak to anyone who is listening (CQ). Somebody else who hears the call may answer, and you will then start talking. Usually you would give him a signal report, since he always wants to know how his radio sounds to the other guy (it is a matter of great pride), and then identify your location and your name. The other party will do the same, and then you can chat about whatever you want (although most hams stick with ham issues like equipment details at first). You can talk about anything, but the govt has strict rules about obscenity and so on. Most of the time you are speaking one to one with one person.
There are also nets which are probably like a chat-room where each person takes a turn in a rotation and many people can be participating. Usually these are done via big repeater stations run by clubs that allow a weak portable station to be reamplified and broadcast over a large region so everybody can hear. Many times during commuting hours, people will be on for a half hour or so with a regular gang.
In the days before cell phones, if there was a road emergency, one of the hams could call for help from his phone (at home or work), if he heard a distress call.
Even today, in times of catastrophes and disaster, when power is out, hams will be the only communication in the middle of an earthquake or flood or similar. There are hams who do special training for these emergencies.
Every summer, there is a general nation-wide simulated emergency drill where one must assemble stations that use no power lines, but are either solar powered or generator powered (some even attach a generator to a bike and use human power), and are located out in fields, and one has 24 hours to set up the stations and antennas, and then 24 hours to make as many contacts as he can all over the world for points. These contacts are extremely short, so one can go on to the next and get more points. It is basically also an excuse to go camping with a radio, and is extreme fun. Clubs set up tents and make a mishmar like on Shavuos to operate around the clock, and barbecue and sit on lounge chairs while it’s someone else’s shift by the radio. There are loggers to keep records, and people to greet newcomers and the general public. It is also a major kiruv event for ham radio. Points are also awarded if you get a politican to visit your club and get into the papers, etc.
Believe it or not, this is a tremendous amount of fun. It is called Field Day. And there is a remez in the Gemara where it says Am Shebasodos.
Hams have been licensed as young kids, and there are people who are over a 100 doing it. Whenever you speak to someone, you usually exchange a post card with your station callsign and a design or picture that confirms details of the contact such as time, frequency, power, station type, etc. People collect them and put them floor to ceiling on their walls. If you get one from every state, you can get a special award. Same if you get one from 100 countries.
It is a whole world out there, truly a fascinating hobby. Once you get bitten by the bug, it is hard to shake it. In the club I belonged to, there were about half a dozen frum guys, and quite a few other Jewish fellows, as well. You don’t need to belong to a club, though, and can do everything on your own, as well.