The symbol commonly known as the pound sign (#) has a long history and lots of names and uses, including “hash.” Did you know it’s also called an octothorpe? It used to be best known as the number sign, as in “Please leave your phone #” or “Contestant #6 is disqualified.” The Wikipedia page has a pretty comprehensive catalog. One of my most frequent uses for it is to indicate a space when editing or proofreading a document, as shown here.
I’m guessing it came into use in the social media context because it’s the symbol used to label a specified location on a page. Hover your cursor over the paragraph mark at the end of this quip and you will see that it marks the tag that points to this specific post.
So—hash mark used to denote a tag—“hashtag.”