Do you need to have a generator or an app of some sort that would convert the Textile markup you did to its equivalent HTML?
Yes to both. Or mostly, depending upon a potential inaccuracy in your question.
Textile is just a simplified markup convention. Browsers won't do anything with it; as far as they're concerned it's just text. You'll need a pre-processor of some sort to generate HTML from it. Some text editors support this directly, there are command-line scripts and web-based tools that'll do it, and probably any major content management system you run across will have a plugin or sometimes native support for it.
The mostly is that Textile is not for generating pages, only content; it's primarily intended for text. You can't create an entire HTML document(eg.