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"Local storage" is referring to the DOM property Window.localStorage, which is what GM:S is using behind-the-scenes. Your browser stores it wherever it pleases (Firefox, at least, puts it somewhere in your profile folder inside .mozilla; can't speak for other browsers).
working_directory is the folder that holds all the files of your game (by default, the value is "html5game/").
To complete the above answer about localStorage in Firefox, you can find, edit or delete data by opening the browser's console > Storage > Local Storage.