RAR stands for Roshal ARchive. It is a proprietary archive file format that supports data compression, error recovery, and file spanning. It was developed by a Russian software engineer, Eugene Roshal (the first letter of his surname contributing to the name of the archive format), and is currently licensed by win.rar GmbH.
The filename extension used by RAR is .rar for the data volume set and .rev for the recovery volume set. In previous versions, if a RAR-archive was split into many smaller files (a "multi-volume archive"), the smaller files used the extensions .rar, .r00, .r01, .r02 etc.
Version 1 and 2 archive files were often used in conjunction with a parchive file archiver to create parity files for error recovery when using less-than-perfect file transmission and storage media such as newsgroups, satellite transmission, and optical discs. Version 3 has eliminated the need for third party post-processing.
Read more about RAR: Compression Algorithm, Versions, Software, Comparison To Other Compression Algorithms, RAR File Limitations