JSTOR, in a nutshell, is just another database of scholarly articles on a variety of topics. You could also say it’s a storage place for journals, thus JSTOR. (See, even scholarly sorts can’t spell 🙂
For the most part, only academic libraries and large public libraries subscribe to JSTOR, but if an article you are seeking pops up in a search engine with a JSTOR location, ask at any library reference desk. Librarians Know Things and, more to the point, know how to find things.
P.S. A database can be much more than a collection of articles. If you want to know more about databases, without screaming, visit here and here. If it helps, online library catalogs can be databases, mailing lists can be databases, but they can also be … no, I won’t make you scream. (But I will whisper spreadsheet, field, file structure, ….)