
This is a mystery that dates back to 2296, while at present, we read year 3305. That is a very long time for Raxxla to remain hidden and unsolved.
It has been object for a multitude of expeditions, searches, theories, fictionalizations, stories and lies.
To address the lies first; many have claimed to have found Raxxla, even claiming to have proof for their discoveries. But these claims still stands unproven. None has come forwards with solid proof of any kind.
What is Raxxla?
Raxxla is perhaps the biggest mystery of the Elite Dangerous universe. And perhaps the most obscure. There is hardly any information about it whatsoever.
The only lore reference to Raxxla is contained in the original Elite novella “The Dark Wheel” by the late great Robert Holdstock.
Rafe chuckled and shook his head. ‘You see, that’s the big question. Your father was chasing the mythical planet Raxxla. Does it exist, or does it not? If it does, then on Raxxla there’s an alien construct that’s a gateway to other Universes, and all that’s in those Universes in the way of bounty, and treasures, and aliens, and life . . .
From The Dark Wheel by Robert Holdstock
‘Jason Ryder was convinced that Raxxla existed. That’s why he trained for, and became a part of, the Dark Wheel, the legend-seekers. I hadn’t heard much from him or about him for some time until just before he died, when he told me he’d found evidence for the real existence of Raxxla. He came back from Deep Space to get a proper team together . . . ‘ Rafe smiled bitterly. ‘But just before he was due to go back, he decided to take a safe-worlds holiday jaunt with his son . . . and an assassin was waiting for him.’ ‘But why?’ Alex asked. ‘Why kill him for finding Raxxla?’
‘Because there are people on Raxxla already. This is only a guess, mind you, but from what happened to Jason I’d say it was close to being right. We’ve long suspected that a corps of élites lives there, and are exploiting the gateway. They’re powerful, twisted men. Powerful enough to hire an assassin to kill the threat to their dominance.
This novella is however, sadly, no longer considered canon for Elite Dangerous, so this description of Raxxla can not be taken literally.
Having said that, most people seem to think it is fairly accurate.
The Dark Wheel is an in-game minor faction seemingly based in the system Shinrarta Dezhra. And commanders have been reporting missions for this faction with specifications referring to “The Great Mystery”.

So far, however, it seems that these missions have been simple cargo-drops, and it is not certain that the now known Dark Wheel faction is the same as the Dark Wheel community of Elite pilots from the novella.
There are two bits of information that has come from sources outside the game and lore:
There will be no clues.
Michael Brookes
It’s out there and we know where it is.
David Braben, speaking for the Frontier Developments crew
Some more speculations about what and where Raxxla is can be read over at Canonn Research, particularly the segment with Drew Wagar’s lore.