The Altar of Despair is reached by breaking a window next to the Lumenflower Gardens lamp.
There is currently no official lore mentioning Altar of Despair.
Once you drop out of the window into the area you kill the two blue aliens and then proceed down the elevator which leads to Ebrietas Daughter of the Cosmos.
For information on the boss fight, go to Ebrietas' page.
This is an optional area.
If Annalise is slain (either by the player or by Alfred) and queenly flesh is acquired, interacting with the altar allows you to resurrect her. She would appear in her normal position in Cainhurst Castle afterwards.
(Work in progress!)
Rom's corpse is found here for some reason.
It is hinted in the official artwork that the Altar of Despair is the entrance to the land of Isz, where Ebrietas is also found.