Vex are spread through varying realities, not just our own. It is not sure if they have found a way to tie these realities to our own or if when the Traveler arrived it somehow overlapped these realities. This is what caused the billions of years old Vex ruins to appear on Venus. This is also what connected our reality to the Vault of Glass.
When it comes to describing the Vex and how they work it becomes difficult. The Vex travel through time and space and can cause great and horrible events to arise. The Vex have tried to re-write time itself in our reality but the Guardians have stopped them, as far as we know. The Vault of Glass is another power however. Every reality, every timeline, flows down a valley as rivers. These rivers run parallel to each other, never meeting. Some, like the Exo Stranger and the Vex, have learned to cross from one river to the others. The Vex created the Vault of Glass and pulled all of those rivers together in point. At that point the every moment of every timeline existed in one moment. The Vex could look through the timelines and see what must be done to assure their victory.
Within the Vault itself the Vex have complete power. This is their reality and they decide what should or should not exist. There are beings in the Vault: The Templar, Oracles, Gorgons, Gatekeepers and Atheon, that harness to ability to erase you from time itself. If you die in the Vault you won't only die, but you will be erased from time and no one will remember you. The paradox of the Vault is that everything that happens in the Vault is happening, yet to happen, and has already happened.
A fireteam entered the Vault of Glass, only three of them are known to us: Kabr, Praedyth, and Pahanin. The team entered the Vault but only one left the Vault, Pahanin. He speaks of entering the Vault Alone but knowing he could not be alone. The idea that someone could have been erased from time and his own memory tore at Pahanin.
Inside the Vault Praedyth was lost in time and Kabr broke the Vault. In the Templars Well Kabr broke the Vex and drank of their minds. He began to see as the Vex do and with this knowledge he created the Aegis. He took the Vex and turned them into a shield and infused that shield with his own dying light. This Aegis would defy the Vault of Glass. It would define its own reality within the Vault that the Vex could not predict or challenge.
Praedyth found himself lost in the Vault and was put within a cell that is guarded by the Gorgons of the Vault. There he worked for years trying to create a communication device, hoping to reach out to others, hoping to escape the Vault. His Ghost appears to have traveled through time and has records that were recovered by Future War Cult that tell of moments through out time. They speak of someone inside the Vault who stood outside their cell. She was always there, in every timeline and every sliver of reality, she was always there and she was always carrying a gun.
The weapon no time to explain was recovered by Guardians and it has sevearl theories around it. One of those theories is that it was built by Praedyth and has skipped through time until it was found.