The Empty White Dawn (or EWD) is the outcome of Albus claiming The Light at the end of the events of PROLEGOMENON, in an attempt to save the players from the destruction of Dodecastratum and their SEED session.
EWD is capable of completely removing universes from existence, and - even when broken down into small shards - its power is still able to influence and take over others, puppeting them to destroy everything in their path. It has also been granted a Delegation by the SEED game (Delegate of Absolution & Dedication)
At the end of Ends of the Garden, it's shown that EWD is a separate entity from Albus in some way - when Ace tells them to let it out, it physically spills out of Albus' body. It's a mixture of The Light's corruption and Albus' freedom of sentience (and thus freedom to feel) granted by Cherry Thaxton's modifications to the SEED session they play during PROLEGOMENON.
While EWD appears in many stories across the Garden, it only exists for a very short time overall (once when created during PROLEGOMENON's Episode 5, and again in Ends of the Garden when revived by the players). However, it does possess the ability to influence people who hold even the shards that it is broken into at the end of PROLEGOMENON's story, which is what results in Yua Matsuo destroying the universe that Dodecastratum is in. These vessels are referred to as Dawns, in order of which they're "influenced".
List of vessels for EWD