Wordpress - allow editors to edit menus?

add this to your theme's functions.php:

// add editor the privilege to edit theme

// get the the role object
$role_object = get_role( 'editor' );

// add $cap capability to this role object
$role_object->add_cap( 'edit_theme_options' );

---

Update (suggested in comments):

You probably shouldn't do this on every request, AFAIK this causes a db write. Better on admin_init and only if !$role_object->has_cap('edit_theme_options')

EDIT: update for WP 4.9 & only hiding menu items for Editor

If you want your users to be able to change the navigation menu, but not the other options under appearance: use this

// Do this only once. Can go anywhere inside your functions.php file
$role_object = get_role( 'editor' );
$role_object->add_cap( 'edit_theme_options' );

You can comment out this entire code after you have refreshed your admin panel, because the above code will make persistent changes to the database.

You now have all the options under appearance visible to the editors. You can hide the other options like so:

function hide_menu() {

    if (current_user_can('editor')) {

        remove_submenu_page( 'themes.php', 'themes.php' ); // hide the theme selection submenu
        remove_submenu_page( 'themes.php', 'widgets.php' ); // hide the widgets submenu
        remove_submenu_page( 'themes.php', 'customize.php?return=%2Fwp-admin%2Ftools.php' ); // hide the customizer submenu
        remove_submenu_page( 'themes.php', 'customize.php?return=%2Fwp-admin%2Ftools.php&autofocus%5Bcontrol%5D=background_image' ); // hide the background submenu


        // these are theme-specific. Can have other names or simply not exist in your current theme.
        remove_submenu_page( 'themes.php', 'yiw_panel' );
        remove_submenu_page( 'themes.php', 'custom-header' );
        remove_submenu_page( 'themes.php', 'custom-background' );
    }
}

add_action('admin_head', 'hide_menu');

The last 3 lines in the hide_menu() function are theme specific for my theme. You can find the second parameter by clicking on the submenu you want to hide, in the admin panel. Your URL will then be something like: example.com/wp-admin/themes.php?page=yiw_panel

So, in this example, the second parameter for the remove_submenu_page() function will be yiw_panel

In WordPress 3.8, this would be better code than the current accepted answer.

/**
 * @var $roleObject WP_Role
 */
$roleObject = get_role( 'editor' );
if (!$roleObject->has_cap( 'edit_theme_options' ) ) {
    $roleObject->add_cap( 'edit_theme_options' );
}