There is no cake here
By splitting the world into sectors (think rooms) and portals (think doors) one can cull away non visible sectors. If a portal leading to a sector is not visible then nothing in the sector is visible and does not have to be drawn. If you see the portal then all portals need to visible inside the first for you to be able to see further away sectors. Like a house with doors.
Early version of portal engines had convex sectors to simplify the hidden surface removal.
Building a 3D Portal Engine - 2009