RAR is a native format of WinRAR compression software originally developed by Eugene Roshal and nowadays by RARLAB. The RAR files have typically a file extension of .rar, but in case of multi-part files, the extension can also be in form of .r00, .r01, .r02, etc. or .001, .002, .003, etc.
In case you have found a file that has an extension of .r01 -- where 01 can be any number -- it means that the file is not a stand-alone RAR archive itself, but part of a bigger RAR file that has been simply split into smaller files. In order to extract such file, you need to obtain all other parts of the archive as well and typically place them in the same folder on your harddrive before opening the file (actually any of the files will do).
RAR is commonly used in P2P networks and in "scene releases" due the fact that it provides more convenient multi-part processing and better compression ratio than its main competitor, ZIP. RAR files can also be secured with a password and the protection mechanism used in RAR files uses AES-128 encryption scheme, making them very hard to "crack".
In order to make RAR files or extract their content, you need to download WinRAR which you can download from here.
Related software tools
WinRAR is a powerful archiver and archive manager.