Selective Calling is as the other have stated. It is a method to reduce fatigue of the pilots. As one of these pilots, it is great. The folks you are listening to is not really Air Traffic Control, rather a private company paid to supply the communications. On North Atlantic Routes, there can be a hundred aircraft on the tracks at any given time. We must report our positions every so often while crossing the oceans of the world and must do so on HF frequencies.
In the very old days before selective calling, pilots had to monitor the HF frequency constantly, and they would have to listen to not only the static of an open squelch, but the constant "position reports" given by the other aircraft.
Selective Calling is simply a manner in which the pilots can turn the volume all the way down, or deselect the HF from the audio panel (speakers/headsets) while allowing the receiver to continue to work. When the base station operator desires to call us for any number of reasons, they first send out the two tone (actually two blasts of dual tones) page. This causes a chime or light or both to go off in the cockpit, indicating that someone is calling us. We can then reselect the HF radio on the audio panel and say something like "November 129 Quebec Sierra answering sel call". As you move across the the ocean, you go in and out of various radio operating stations. New York, Shanwick, Santa Maria, etc. Normally, your sel call code is in the flight plan but typically on first contact with a new radio operator, they will either ask for or automatically send your sel call as a test to make sure it is working.
You will here pilots request a sel call check by stating something like "November 129 Quebec Sierra request sell call check Bravo Victor Echo Juliet" That is the 4 letter designator for their aircrafts sel call decoder (BV-EJ).
As to ATC, as I said, these are simply middlemen who make phone calls to the actual ATC system. If a pilot requests a higher altitude, the radio operator will call real Air Traffic Control and ask if it is OK. This is a prime use for sel call. When the guy gets permission, you will hear them first send out the two tone page. When the pilot answers, you will here something like "ATC Clears November 129 quebec Sierra to Flight Level 380, report reaching".
All of these contacts is so the ICAO governing Air Traffic Control Agency can track your position as you move across the ocean and insure nobody else is at you same altitude and location, a good thing. There is no radar coverage over the ocean, so except for military ships and aircraft, nobody knows where you are. They know where you last reported, your speed, and your estimate to the next position report, and them computers at ATC can predict your location at any given time.