These days, the effect has gone a step ahead. Now, it is not associated with Medium-like websites. Now, it is being used in all kinds of websites. All thanks to its space-saving, dynamic style.
The works like this, it stays folded up and it is nowhere visible on the whole web page. But when the user clicks a particular button usually identified with three hyphens, even though trend is changing, the menu pushes the whole canvas (web page) away and loads itself.
This kind of menus are extremely handy if you are designing a responsive web design for mobile devices.
Pushing is not necessary however, the menu can slide over the web page, but then it will hide the contents below it.