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.
When in doubt, ask Wikipedia: [Pair Programming](http://en.wikipedia.org/wiki/Pair_programming). The general idea is to have one person writing code while the other scans for mistakes and cohesiveness.