Amateur radio, or ham radio, is a technical, explorative and contact-seeking hobby practiced by some three million people worldwide. In one sense it is similar to the various walkie-talkies that are freely available; in another, it is very different. In order to operate an amateur radio transceiver (that's shorthand for a combined transmitter and receiver) you are required to have a license, but that license gives you the right to do a lot more than just talk on the radio to your next-door neighbor or friend across town. The choice is up to you whether you want to talk to them using radiotelephony, or if you prefer to chat with someone on the other side of the world using for example Morse code or digital transmissions, which looks and acts similar to chatting over the Internet except that everything goes over a radio link.
While it is very free-form, amateur radio is also regulated. There are both international regulations, such as the ITU Radio Regulations, as well as national regulations. By and large, however, the regulations are the same throughout the world: radio amateurs enjoy access to mostly the same frequency bands, call signs are made up in a similar way, and the purpose of amateur radio regardless of which country one is in. Regardless of where you are, amateur radio transmissions have to be identified using a uniquely assigned call sign. For example, my call sign is SM6YBY (the series SA-SM, 7S, 8S is assigned to Sweden; I am in district 6; and YBY is simply a sequentially assigned identifier); this uniquely identifies me in the world of radio amateurs.
Yes, I did say frequency bands above. Most radio services are allocated as specific frequencies for a given purpose, most often referred to as channels, but radio amateurs have large bands within which many governing bodies place no technical restrictions on what kind of transmissions can be made. This has led to the adoption of so-called band plans, which are recommendations for where in each frequency band to use which transmission mode. This is done both to reduce conflict, as well as to help two people using the same transmission mode (Morse code telegraphy, single sideband radiotelephony, frequency modulated telephony, PSK31 digital transmission, and so on) find each other.
Radio amateurs talk of channels, too; but in our case, it is just a convenient way to express a frequency or frequency pair possibly combined with an implicit or explicit transmission mode. It is much easier to say "let's switch to R1" than "let's switch to the 12.5 kHz-wide frequency modulation repeater with input frequency 145.025 MHz and output frequency 145.625 MHz", but to a European radio amateur the meaning is the same. The channel "3750 kHz", likewise, is a convenient way to express the lower sideband 3 kHz frequency space with a suppressed carrier at 3750 kHz. If someone is using, say, 3752 kHz already, you can just as easily move down slightly to 3749.5 kHz to reduce interference.
Besides being a fun hobby, radio amateurs are also often called upon to provide various forms of disaster relief and other public service communications. This is more often done within the amateur radio service in for example the United States, but even in countries where emergency communications is handled by other means from a legal point of view, because radio amateurs continually practice and hone their radio communication skills, those providing the service to the community are often radio amateurs as well as whatever other certifications they might have.