This is customisation ( a really nice one ) that isn't offered in the regular Lay Theme options provided.
This goes beyond my level of Forum support, you may wish to seek the aid of a developer if you are unable to create this yourself.
However i would be happy to show you the basics of what is happening here.
Let's take a look at "About" as an Example.
When clicked - the class "active-about" is added to the page
The About area has always existed, but it has been hiding off to the left side of the viewport.
- It has a width of 50% and has been sitting ( -50%) off to the left
When the class "active-about" is added to the page, the browser receives some new CSS information that makes it visible to the viewer,
Transform property not added:
Clicked: Transform property added:
The smooth gliding that occurs is due to the transition css property:
If there were no transition it would just blink on and off the screen without the "transition".... :)
For additional information regarding CSS:
I hope this helps & good luck on your Lay Theme journey,