Question: This term seems to be quite in use in English-speaking communities. I'm curious what it is? Is it like two students code together on a single PC or what? Is this organization (whatever it is) is only used in US?

Answer: 
Pair programming is one of the main practices in Extreme Programming (XP). It does literally mean two people working on one computer, usually one at the keyboard (often referred to as the driver) and a partner (referred to as the passenger or shotgun). It is reputed to improve productivity and the quality of the generated code as well as enforce group ownership of the code - another tenent of XP.
An extension of Pair Programming sometimes used by practitioners of [Test Driven Development](http://en.wikipedia.org/wiki/Test-driven_development) is [Ping Pong Pairing](http://c2.com/cgi/wiki?PairProgrammingPingPongPattern).

Ping Pong Pairing works something like:  

* Write a failing test (developer A)
* Implement code that makes the test pass then (optionally) [Refactor](http://en.wikipedia.org/wiki/Refactoring) (developer B)
* Write a failing test (developer B)
* Implement code that makes the test pass then (optionally) Refactor (developer A)
* and so on...

One of the benefits of Ping Pong Pairing is that it's tough for either developer to sleep very long ;-)