The Great Evil Beast was formed when God uttered the words "Let There Be Light" and came to embody all the darkness in creation as well as everything that opposed the light of the Presence (which is DC universe's version of God) - however despite its immense power the Great Evil Beast was still a newborn entity and thus was easily defeated by the Presence and contained within its own realm.
When the events Crisis on Infinite Earths took place, a group of mystics named the Brujeria attempted an occult ritual designed to contact the Great Evil Beast but it went horribly wrong and the entity awoke as a furious beast, unable to grasp its power and becoming confused as to its existence.
The Great Evil Beast would encounter Etrigan, Dr. Fate and the Spectre - Etrigan taught the entity that Darkness was Evil, Dr. Fate told the entity Evil was Despisable and the Spectre finally told the entity about the concept of revenge: these new lessons angered the Great Evil Beast despite the heroes being well-meaning and it launched an assault on Heaven itself in order to get answers as to its existence from the Presence itself. Along the way the Great Evil Beast decimated anything that got in its way and was so powerful that Lucifer, Azrael and Beelzebub formed an alliance to defend themselves should the Great Evil Beast decide to attack Hell as well - somewhat ironically another batch of demons known as the Demons Three decided to do the opposite and allied with the Great Evil Beast, seeing it as the ultimate sin and evil (which technically it was). Finally, Swamp Thing, readied by his journeys into the Parliament Of Trees and his dealings with John Constantine, sought the entity out of his own free will, whereas all other beings had been engulfed after being soundly defeated. The entity listened as Swamp Thing gave what little he had, lessons that implied darkness was in its own way as needed as light, and had a place in the cosmos after all. It told Swamp Thing to leave him in peace, as he had entered, and prepared for what it called a great and final ending.
However as the Great Evil Beast stormed the gates of Heaven itself the entity extended its hand and much to the surprise of everyone the Presence did likewise - this climaxed in the two beings merging together into the perfect balance.
The battle was not without its price. Doctor Fate killed one of the Demons Three. On the more heroic side, Golden Age magical hero Zatara sacrificed his life to save his daughter Zatanna, and Sargon The Sorcerer also met his end. John Constantine lost some of his oldest friends in the campaign to stop the Brujeria, while his ally Mento (Steve Dayton, formerly of The Doom Patrol and an ally to The Teen Titans) glimpsed the smallest portion of the Great Evil Beast and went insane, actually becoming a villain for several years.
In later issues showing the afterlife in Swamp Thing, he would glimpse the joined hands of the darkness and the Presence.
Powers and Abilities
The Great Evil Beast was almost omnipotent - it seems that the only being that was above it in power was God himself and it is implied that the Great Evil Beast was God's dark-half, it is not known whether or not the Great Evil Beast still exists or not after it merged with the Presence but like all omnipotent-types the answer is likely beyond our understanding.