A tarball is a tar archive file, similar in some respects to zip or rar archives. Tarballs are usually compressed with gzip (ending in .tar.gz, or .tgz) or with bzip2 (ending in .tar.bz2). Unlike zip, tar is not able to compress or encypt, but only pack files together. It is for this reason that other utilities are used to compress tarballs. Encryption is not usually used, because tarballs are typically used to distribute things openly, but it can be applied in the same style as compression: use an encryption tool on the archive file.
Most software source codes are distributed as tarballs.
See tar for how to extract tarballs, as they are just normal tar archives.