Disambiguation: for the series itself, see Deca-Dence.
Deca-Dence is a gigantic 3000m-high mobile fortress created by humans to counter the Gadoll.
Note: This page contains spoilers.
The name spells out "Decadence", reflecting humanity's almost doomed state at the attacks of the Gadoll. Deca-dence is also the name of the game the cyborgs play. When they log in, they receive an Avatar in the fortress. Using that avatar, they can fight Gadolls.
After the destruction of the Deca-dence fortress, the machine becomes a city called Deca-dence City. New areas and hobbies, from farming to a battle arena, are introduced for the cyborgs to entertain themselves while living with the humans.