The Boundary, sometimes referred to as Gehenna, is the space where all timelines intersect. It is a vast dimension that stands outside of time, and is only accessible through a select few devices, but the main entrances lie in the cauldrons that populate the world. Both the Azure and Amaterasu sit deep within the space.
There are very few things that exist within the Boundary but there is one constant - seithr, a vast and corrupting substance that is in a seemingly infinite supply within the dimension. As it is the place where all timelines intersect, nearly infinite information is present inside the dimension, and it connects all timelines. Theoretically, a person can jump between timelines, time, and possibilities using the Boundary as a conduit for transport but it is an almost impossible feat as the Boundary corrupts the mind, soul, and body of anyone who even stands near its entrances; to even touch the Boundary is a death sentence for most.
The Boundary is pitch black, only faintly lit by the blue glow around those inhabiting it. There appears to be a form of geography within the dimension as one part of it is called The Edge, where both Yuuki Terumi and Hakumen slept after a battle shortly following the Dark War. Hazama's name is taken from this location 
Lotte "Roy" Carmine's obsession with the Boundary led to his body eventually becoming Arakune after he was manipulated by Terumi into physically jumping into a cauldron. His soul was allowed to lay within the Boundary and study it further so long as his physical body remained in at least one possibility - towards the conclusion of BlazBlue: Central Fiction, Roy was able to stay in the Boundary without Arakune anchoring his soul from being eroded. Despite his extensive research, very little is still known about the Boundary in any possibility, however.
Only one barrier stands between the Boundary and the many worlds, and that is the Phantom Field, previously known as the World of Tsukuyomi. It was a complex plain of space that was created by Es, and previously managed by both Nobody and Nine the Phantom before they passed away. Es originally created this space to prevent anyone from accessing the Boundary and finding the Embryo, which was last seen inside the Phantom Field.
Before recorded history, a Black Beast rose out of one of the cauldrons, but was subdued by the Azure Shrine Maiden luring it back into the Boundary by sacrificing herself. Despite its corrupting nature, Makoto Nanaya, Relius Clover, Naoto Kurogane, Hazama, Nu-13, Hakumen, and Terumi have all travelled inside the Boundary and survived. There are a number of contributing factors, such as the Power of Order, sheer luck, and/or an incredible willpower, that have allowed people to survive being within the Boundary for extended periods of time. Because a Black Beast is essentially a walking cauldron, anyone eaten by one will be taken inside the Boundary itself.
Rachel Alucard was once an Onlooker of the Boundary, titled Amatsumugi, but she abandoned that duty at some point; Takamagahara, Amane Nishiki, Amaterasu, and Rachel herself all have the ability to Observe different timelines present within the Boundary. Kokonoe has been known to store information banks deep within the Boundary as backups in case her memory was compromised by the time around her being distorted. Sound can be transmitted through the Boundary as Es was able to find Amaterasu thanks to it emitting a unique discover call.
The place of Origin, and the place where Murakumo Units are smelted. It is a world beyond the Gates of Sheol. It’s a complex space connecting all dimensions, and it’s filled with seithr.
The Master Unit ‘Amaterasu’ sleeps in the deepest part of this world, and only the ‘Successor of the Azure’ can comprehend where to find it. 
The space between the Boundary and the present world. The notion of time is vague in this place, and Hakumen was recovered from here. Entering this place causes normal existences to vanish, but thanks to Hakumen’s strong force of will and the Susano'o Unit, he managed to return despite the loss of most of his power. 
A plane of reality which contains a seemingly inexhaustible supply of seithr. It exists outside the universe the world currently inhabits, and is an enigma wrapped in a mystery. It is sometimes referred to as Gehenna 
- BlazBlue: Calamity Trigger
- BlazBlue: Central Fiction, Library Mode, Location #038
- BlazBlue: Central Fiction, Library Mode, Location #043
- XBlaze Lost: Memories, TIPS, #28