Amateur radio, also called "ham radio", is a hobby of many many peoples throughout the world. Every licensed Radio Amateur has a call sign that is used to identify his and his location. Call signs consist of a prefix and a suffix. The prefix is usually composed of one or two letters and a number. Prefixes are allocated to countries around the world such as DL or DJ in Germany. While the prefix uniquely identifies a country the suffix is unique for the individual. So in Germany a call sign DJ8KM has DJ8 as the prefix and KM as the suffix. This call sign is unique throughout the world.
Radio Amateurs use radio transmitters and receivers on specific frequency to communicate with other Amateur radio operators.
Amateurs use a variety of transmission modes, including Morse code (CW), voice, radio teletype and data.
Talk around the world is only one of activities of ham radio. Another activities are e.g. technical experimenting, DXing, amateur television, Slow Scan TV, satelite communications (Hams have their own satelites), contestings, Packet radio...
Part of the fun of amateur radio is collecting cards, called QSL cards, from other amateurs that you have contacted on the radio.
All countries have their own national Amateur Radio organisation, like DARC in Germany. National societies also cooperate through the International Amateur Radio Union (IARU).
Licensing requirements are different in every country with different rules. All hams in Germany are licensed by Bundesnetzagentur.
There are many ways to preparing for and taking your ham radio license test.
A good way to get started in Ham Radio is to find a club in your region to answer your questions and provide information on getting licensed and then getting on the air!
Shortly speaking: Amateur radio is a community of people.