A tarball was a term describing a backup archive file on a computer.
When Peter Kingsley's men raided Alex Hewitt's apartment, they took much of his computer equipment. However, he kept a hard drive hidden in the base of one of his drawers that contained a tarball with all of his software and audio files relating to the Cyprus recording. When Jack Bauer and Sherry Palmer made a deal with Alex to testify, he retrieved the hard drive and told them they would have to wait for the tarball to decompress. ("Day 2: 5:00am-6:00am")
