How does group really works?

I tried to make new group like this:

But somehow it still shows some other menu like institutions and all. How does it really works?

Menus are visible to all users if no group is assigned.
I suspect that “Institutions” menu doesn’t have any group assigned, so that’s why everyone who can see the Health menu can also see it.

So I can’t hide the menu? Is there any better solutions?

You can either create a new group and assign it specific permissions for that menu, or edit an existing group. If a menu isn’t assigned to any group, it will be visible to everyone who has access to its parent menu. So, if you want to restrict access to the Institutions menu, assign it to a group that only the desired users belong to.
Also, there’s the option to deactivate the menu if you don’t want it displayed to any user.