It meant that you'd download it from one BBS, then upload it to the next for those sweet file sharing credits. That was my standard method for getting software until 1994 or so.

It was very common to find that kind of software on magazines' CDs. For example, I installed for the first time WinRar after finding it inside a promo-CD of a magazine (I don't remember the name). I guess the 'share' was because the license was(is) permissive in terms of distribution (internet mirrors, magazines' CDs, promo floppies, etc...) and after a certain amount of time, it was required to pay the license to keep using the software.

It probably related to the practice of sharing useful tools on CDs. Before the internet the highlight of my month was the CD ROM that came with computer magazines and was loaded with sharewares and freewares.

You could "share" the demo/lite version with your friends, unlike boxed software where any copy was prohibited.