"fapstation" is a synonym for
PC or Computer.
Your PC is the place where you
fap most frequently, so it is your fapstation. The term was
first used by the Youtube-Director GuitarMasterX7, in a video where he showed all his equipment.
This is my room, here you see my
TV, and there is my fapstation.
I bought new fapstation, I needed a new one for all the upcoming
games this
fall.