I got a call from one of my people the other day: "I am supposed to open my Hamburger Menu. What in tarnation is that? Do I need to hit a McDonald's?" I laughed and explained it is just a term for modern day application menus.
Those of us who computed pre-Windows recall having to remember what each function key did. We used templates for every program, reminding us which function key corresponded to what menu command. When Windows came out, using function keys was replaced with using pull down menus, accessed via the ALT key or through a mouse click. We got used to using pull down menus. We liked pull down menus. But then they started disappearing.
The "Hamburger Menu" is what has begun replacing pull down menus. This is, in part, due to the "Mobile Revolution" and the proliferation of smartphones and tablets. On mobile devices, touchscreen and taps replace mouse clicks. Pull-down menus were difficult for fat fingers. Mobile devices do not have a lot of screen real estate either, leaving little room for a menu to stretch across the screen.