Javascript didn't need a plugin, unlike Java, and could directly alter the page contents. One of the first heavy uses was Google Maps, interactive JS-based applications took off at that point. Then with an army of web developers (meaning in browser), Node took off when it handed them a way to work on the backend in the same language.

The iPhone came out after JS heavy pages came into existence, and might have accelerated the end of Flash and Java applets but the trend was already there.

Gmail was the original AJAX woah! JavaScript application.