R is a programming language designed for use in statistics. (Perhaps there are still a few letters of the alphabet as yet untaken for single-letter programming language names, but if not, there's always Unicode to be trawled for name-worthy characters.) It is an interpreted language, and the interpreter is distributed as free software. Built-in features include the ability to generate graphs and plots, as well as the ability to store an entire array (or "vector") in a variable and do mathematical operations on all elements of the vector with a single operator (similarly to APL). It can also do complex-number arithmetic (similarly to Python).
Apparently the .R file extension is generally done in uppercase.