Out of curiosity what is it? Neither the store link or this one seem to explain. Is it some kind of citations tracking system? A pdf editor? I'm not sure what the features add up to in total.
It's mostly a tool to manage research literature. It allows you to add works you are viewing in your web browser to collections. Then, you can create bibliographies from these collections. As a researcher I use it a lot, since it makes working with references much smoother. There's also extra features like cloud syncing and most recently an integrated PDF viewer and annotator. https://www.zotero.org/
It's most commonly used by academics for automatically extracting citation metadata from journal article pages from JSTOR, Springer, Elsevier etc. in a structured format (instead of having to enter them manually) and saving them to a local library. Also automatically saves the PDF locally if you have access to it.
It also has a Word add-on that allows you to insert citations as dynamic Word "fields" linked to items in your Zotero Library, so citations can be automatically kept in sync with your Zotero Library and can be easily converted to different formatting styles.
Yeah, fundamentally it helps you manage records of documents. Of course you can also attach PDFs and full text (if you have them), but it's the record that's important.
A common use case is in academia - it helps you track your citations and then output standardised reference lists, which is a pain to do by hand.
Other tools in this space are Mendeley and Endnote.