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.