Here is the technical definition:
Ham Radio, or Amateur Radio, is a radio that is operated in accordance within FCC regulations on specific radio wavelengths or bands. The radio operator can communicate across the world and even to the International Space Station.
Here is the reality:
If you like to talk to people from far and wide, if you like to experiment (or not) with electronics, if you like to be ready for emergency conditions…
Then Ham Radio is a hobby you will like.
A great write up with a boatload of history and trivia is located here: https://www.legion.org/hamradio/definition
Here is a video on the general hobby: https://youtu.be/wDn-6SDxyD4
Here is a video on the 21 Century aspects of the hobby: https://youtu.be/8x6x_6mDVlQ
The full story is at: http://www.arrl.org/what-is-ham-radio