If you had any drop-down menus in your original site, then the company that did the work should have included these as well, but if there wasn’t any there before then they’ve probably not thought about that and left it as a standard menu that will just show everything.
There are ways to get around that, but they do involve a bit of editing and coding to get it done. There’s probably some plugins out there that can give that sort of functionality so I’d suggest searching for something in the plugins area to see what’s around.