These are paradox realms designed by the Nepharites, paradox beings who live on guilt and suffering. When a mage filled with guilt, fear, or pain suffers a paradox backlash, they will send him into a purgatorium, a realm designed to evoke more suffering for the enjoyment and nourishment for the nepharites. Normally these realms are purely mental, the mage seems to go into a deep sleep or coma and cannot awaken. What really happens is that the mage accidentally opens his mind to the Nepharites, who are given full control. In some special cases (like Spirit and Correspondence Paradox), they might enter a purgatorium bodily too, but it is rare.
A purgatorium may look like anything, but is often based on the surroundings of the mage when he suffered the backlash. Things are almost right, but small disturbing details abound or certain things are clearly horribly out of place (like having a torture chamber in the middle of a night-club or gallows with hanged people instead of streetlights on a street). The realm is completely controlled by the Nepharite, who can do anything inside. It can change how it looks, the way it works or what happens. It can turn the mage inside out with a gesture and keep him alive forever. However, nothing that happens inside the realm can have any effect on the outside (unless the mage believes in it strongly enough to create hobgoblins and Quiet making it nearly real). So the Nepharite may kill the mage again and again, but if the mage escapes he's unhurt.
The Nepharite may determine if magick works or not, or how it works. It can turn all magick inside the Purgatorium around, controlling it completely (after all, its just illusions). It is possible to destroy the body of the Nepharite if it allows it, but it can of course reform anytime it wants. However, Nepharites love to give their victims hope and then destroy it. The Nepharite cannot really touch the Avatar of the victim, so the victim will still retain his countermagick and Arete, and purely internal magick (like Mind 1) can't be influenced. But the Nepharites are good at creating mental illusions, making their victims think they can't resist anything.
The Nepharite seeks to evoke more guilt, fear and pain from the mage using any means possible. Plain torture is not the best way to do this, more subtle means are more rewarding. The Nepharite can make the mage meet old friends he has betrayed (or think he has betrayed), place him in the same situation again and again or create scenarios to provoke more negative emotions. The only way to escape a purgatorium is to realize what it is. If the mage stops being guilty or afraid, the Purgatorium will dissolve and he will escape. However, the Nepharite naturally tries to hinder this by adding extra problems when somebody seems to figure it out.
Nepharites may be all-powerful inside their Purgatories, but outside they are just ordinary paradox spirits. Their powers vary, but most are adept at Mind, especially the creation of emotions, illusions and finding weaknesses of people. Some Nepharites are not content with simply dragging mages into their realms, but actively seek them out before they suffer any big backlash. They will try to increase their guilt and pain, and either make them do something that gives the Nepharite the chance to send them into its realm (just voluntarily opening your mind to it is generally enough), or manipulate them to spread more guilt, fear, and pain among others.
Some Nepharites even tempt the mages with promises of power, pleasure or other things. If the mages accept, they are led into their Purgatories and given what they want. These Nepharites feed at first on the gluttony of their victims, and then on their pain when they can't get enough. As the mages become more dependent on the Nepharite, it can start to twist the mages. They have to do more and more to get what they want, and they become more and more debased in their pursuit. In the end they suffer horribly, only upheld by a hope that never will be fulfilled.
Purgatories are not completely evil, some mages claim they even do good sometimes. By forcing the mage to overcome his self-imposed limitations, the Nepharites are forcing them to develop. There have been cases where the Avatar of the mage has appeared before them in the Purgatorium, turning it into an Epiphany. Some Nepharites might even be the Avatars of their own mages! But there is a dark side of the Purgatories too. Some mages fail completely, and become imprisoned forever (this happens also if the body is killed). In that case they become slaves to the Nepharite, who can do as it pleases to them. In some cases they have turned into Nepharites themselves, in other cases they have become snivelling slaves who do anything for the Nepharite to escape more punishment. Some mages have escaped from the Purgatories, but the lesson has turned them less human and more Nepharite themselves.
The Nepharite appears before him (looking like something awful which has escaped from the dissecting table. It is wearing a comfortable costume stained by blood) and welcomes him to Hell, his new home. "Before we start torturing you forever, you might want to meet your neighbors. Here is someone you know, I think. Peter, I think you have met Hans?" On a dissecting table Peter is strapped and several figures in stained surgical dresses are busy vivisecting him. Between his anguished screams he manages to shout to Hans: "You sent me here! You sent me here!"
The Nepharite will start to torture Hans, but the torture is really just an extra touch. The real pain comes from having all his old friends and relatives appear to be imprisoned here, and most of them have appeared here due to his own actions. From time to time the Nepharite drops other friends and loved ones into the Purgatorium (naturally, nobody is real, but they appear real), adding fresh pain. Even better is having Hans try to escape and free his friends, because then he can make a mistake just when they are about to reach freedom, and then they will all be returned to Hell and he will feel more guilt about failing his friends.
The only way he can escape is if he realizes that it's the guilt he feels for his friends and his actions which keep him imprisoned. If he just tries to escape without trying to save his friends or excuse himself to them, he will succeed. He will wake up from his coma.
Example 2: Ylva Carlsson, a Virtual Adept, is being hunted through the dark streets of Stockholm by the Men in Black. She desperately tries to Vector away using her laptop, but she botches and she is sent into her purgatorium. What she sees is just how the laptop crashes, nothing else has changed. She is still hunted by the Technocracy, there are Men in Black behind her, she hears the bark of enhanced bloodhounds and somewhere above a helicopter searches for her with a searchlight. The purgatorium looks exactly like Stockholm, except that there is no help anywhere. There is no one on the streets, all doors are locked, all people are asleep, her laptop has crashed (truly traumatic for a VA) and her allies are gone. The night will continue indefinitely.
The Nepharite, which doesn't appear visibly, directs the hunt after her. As soon as she finds a hiding place, the Men In Black find her after a few moments. However, she has always a chance of escape, so that she can be hunted even more. It tries to give the impression that the Technocracy will kill her outright if she as much as turns around (say by having them efficiently kill a few innocent bystanders who had the misfortune to see the hunt or use some nasty weapons she just avoid by sheer luck), since that is the only way she can escape. She must turn around and face what she fears, not flee it, to escape. Of course, if she does that, the Nepharite will make a last attempt to frighten her into fleeing, by letting her see the unstoppable might of the pursuing technomancers and the futility of resisting them. If she tries despite this, then the nepharite has lost its claim to her and she will awaken.
Example 3: Karl Steen, member of the Order of Hermes, is seeking Ascension. He is obsessed with it, and tries to learn everything about it. At the same time he isolates himself more and more from other mages, who he (quite correctly) suspects wouldn't understand his theories. When he tries to perform a great ritual to summon his own Avatar, he naturally fails and suffers a severe Paradox Backlash.
Before him, his Avatar stands (it is of course the Nepharite). It asks him what he wanted, and as he explains that he seeks enlightenment, it seems to be pleased. It says: "Come. If you can overcome the great dangers before you with your knowledge, will, intuition and power, you will gain it." If Karl hesitates, the Avatar will ask him if he really wants to reach enlightenment or if he is content to remain unenlightened. Quite naturally the mage will follow his Avatar on the quest.
The Nepharite creates a gruelling quest for the mage, with no end. The mage is led through more and more hermetic adventures, where his skills are constantly tested. He knows that if he fails in any part, he will fail completely. He has to solve ancient mysteries, meet allegorical persons, travel dangerous and symbolical paths and so on (for some ideas, read "The Alchemical Wedding of Christian Rosencreutz") If the mage ever seems to tire or hesitate, the Avatar will remind him that perseverance and strength of will are essential parts of the seeking, and if he gives up, he will fail completely. If the mage wonders why the quest is so long and hard, the Avatar will explain that Enlightenment is never easy to reach.
The only way for the mage to escape the quest is simply leaving it, returning to his normal life and abandoning his Avatar. He must overcome his obsession with success and his stubbornness, and suffer the pangs of insecurity as he turns his back on Enlightenment. That's the only way he can reach true Enlightenment.