I use unix distros every day and I started using them a long time ago but I never thought about the provenience of the word "tarball". I tried to search it on the dictionary but I didn't find anything. At this point it could also be a completely invented term but I thought "better to ask".
It's a joke.
tar (Tape ARchive) is the name of the program used to create an archive that contains several files, all glued together.
Tar is also a black and sticky substance obtained from hydrocarbons. It translates to catrame in Italian (from your name, I suppose you're Italian).
Therefore, if you take a bunch of files and stick and roll all of them together via the
tar program, you obtain a tar ball or tarball.