Hello, as stated in a notice you should have in wp-admin, you need to explicitly set a menu from Appearance > Menus for it to work properly in responsive mode.
If you don't set your menu there, WordPress will use a fallback menu which doesn't work well (and simply disappears on mobile).
In mobile mode, the navbar is replaced with a drop-down menu. When you touch it, the menu will appear with your phone's "pull down" menu, which is easier to use on a phone than the "normal" navbar.
You can visit http://demo.iceable.com/silverclean-lite/ from your iPhone to see how it looks once the menu is configured.