Action normally specifies the file/page that the form is submitted to (using the method described in the method paramater (post, get etc.))

An action of # indicates that the form stays on the same page, simply suffixing the url with a #. Similar use occurs in anchors. <a href=#">Link</a> for example, will stay on the same page.

Thus, the form is submitted to the same page, which then processes the data etc.