The usual way to make a menu keymap produce a menu is to make it the definition of a prefix key. (A Lisp program can explicitly pop up a menu and receive the user's choice—see Pop-Up Menus.)
If the prefix key ends with a mouse event, Emacs handles the menu keymap by popping up a visible menu, so that the user can select a choice with the mouse. When the user clicks on a menu item, the event generated is whatever character or symbol has the binding that brought about that menu item. (A menu item may generate a series of events if the menu has multiple levels or comes from the menu bar.)
It's often best to use a button-down event to trigger the menu. Then the user can select a menu item by releasing the button.
If the menu keymap contains a binding to a nested keymap, the nested keymap specifies a submenu. There will be a menu item, labeled by the nested keymap's item string, and clicking on this item automatically pops up the specified submenu. As a special exception, if the menu keymap contains a single nested keymap and no other menu items, the menu shows the contents of the nested keymap directly, not as a submenu.
However, if Emacs is compiled without X toolkit support, submenus are not supported. Each nested keymap is shown as a menu item, but clicking on it does not automatically pop up the submenu. If you wish to imitate the effect of submenus, you can do that by giving a nested keymap an item string which starts with ‘@’. This causes Emacs to display the nested keymap using a separate menu pane; the rest of the item string after the ‘@’ is the pane label. If Emacs is compiled without X toolkit support, menu panes are not used; in that case, a ‘@’ at the beginning of an item string is omitted when the menu label is displayed, and has no other effect.