RAR is a proprietary archive format that was widely used in the 90's and the next decade when the Internet became a popular place to share software and media files. It has better compression ratio than ZIP, has strong encryption and very good error recovery capabilities. I have some memories from my time as a student of keeping a WinRAR binary on a floppy and use it to decompress and compress files transferred from and to the Internet.
I'm not going to debate over FOSS vs. commercial software in this post. If we weigh in such arguments, there are no reasons to use anything else than the LGPL licensed 7Z (p7zip) or tar with bzip2, gzip or xz (and their parallel variants), but that was not the point of this post.
There is also a freeware unrar program and libunrar library available for Linux and Unix (for Fedora in the rpmfusion repository), but it is only able to extract files from RAR archives.
To be able to create RAR archives, you have to use the official software from RARLAB. You can use it for 40 days. After this you have to buy a license key. The license is fair; software upgrades have been free (at least until now).
To easily install the RAR program (instead of downloading from the official web site and manually install it) on Fedora, there is a repository available at negativo17.org. This way also updates are nicely handled. Just add the repo file:
sudo yum-config-manager --add-repo http://negativo17.org/repos/fedora-rar.repo
sudo yum -y install rar
As far as I can tell from the RARLAB site, the license for WinRAR and RAR for Linux/Unix are the same and the later versions use the same license key. Just put the rarreg.key in your home directory (for a single user license) and begin archiving.