Dungeons were an intricate structure of Aethoria, and the only experience I've ever had with one was the Inheritance Dungeon of Laplace.
From what i knew so far, they were unnatural structures which emerged and started to appear during the invasion all those many years ago. So they were concepts and aspects that have even so deeply tied themselves inti the history books.
The invaders and Demons used various means to travel through worlds, and one of such is by widening cracks between realms and creating 'passageways'.
Those 'Cracks' were later known as Gates. And the "Passageways' became Dungeons.
So put simply, Dungeons were fragmented parts, or tunnels of a different world and realm entirely, and a Gate was the entrance of such a dungeon.