The Jargon File (version 4.4.7, 29 Dec 2003):

tarball
 n.

    [very common; prob. based on the ?tar baby? in the Uncle Remus folk tales]
    An archive, created with the Unix tar(1) utility, containing myriad related
    files. ?Here, I'll just ftp you a tarball of the whole project.? Tarballs
    have been the standard way to ship around source-code distributions since
    the mid-1980s; in retrospect it seems odd that this term did not enter
    common usage until the late 1990s.


The Free On-line Dictionary of Computing (30 December 2018):

tar
tape archive
tarball

    ("Tape ARchive", following ar) Unix's
   general purpose archive utility and the file format it uses.
   Tar was originally intended for use with magnetic tape but,
   though it has several command line options related to tape,
   it is now used more often for packaging files together on
   other media, e.g. for distribution via the Internet.

   The resulting archive, a "tar file" (humourously, "tarball")
   is often compressed, using gzip or some other form of
   compression (see tar and feather).

   There is a GNU version of tar called gnutar with several
   improvements over the standard versions.

   Filename extension: .tar

   MIME type: unregistered, but commonly application/x-tar

   Unix manual page: tar(1).

   Compare shar, zip.

   (1998-05-02)