R is a software platform for statistical computing (modeling, visualization, data manipulation etc)
Initially mainly used in academia, but gains popularity over the years
Other script languages similar to R for statistical computing include SAS, S-Plus, SPSS etc
It is free
The R programming language is a high level script language
That means R executes statements (c.f., commands) from the source code line by line.
Different from lower level programming languages such as C++ or Java, which needs to compile the source code into binary executable first and then execute.
Consequently, you will not be able to run C++/Java code if there are syntax errors (as the code will not compile). In contrast, R execute all statements before the one that contains error.
The R Project for Statistical Computing is a centralized place for
The R software, R programming Manual, and various statistical packages
A good document is An Introduction to R, which tells you
How to invoke R (from Windows, Mac etc)
Data manipulation on simple data structures such as array, list, matrix, data frame etc
File I/O (read and write file)
How to write R functions
Statistical modeling in R
Graphics and data visualization tools in R
Google often helps.