The Dream World is an astral plane best described as the collective unconscious of all Pokémon throughout reality that Pokémon can access while asleep. Unlike the various alternate universes that have been explored, the Dream World is not tethered to any one of these, and seems to exist on a plane of reality all of its own, with communication between universes being possible using it, as was the case between Tagg (In PMD-B) and DS (In PMD-A) during the PMD-R Arc.
It is seemingly infinite in size and scope, made up of multitudes of islands of all sizes and terrain floating in a void akin to the Pokémon world's atmosphere. Most often clear with blue skies and the occasional cloud, the weather and time of day can vary widely.
As the Dream World is, well...dream-like, its reality can only be described as "chaotic". Time can suddenly halt one minute, then several days could pass in the blink of an eye. Gravity is more of a suggestion than a rule, leading to Pokémon walking up one wall while comfortably carrying out a conversation with another standing on - from their perspective - the ceiling.
Impossible structures - such as towers balancing on their tip - are commonplace. One particular practical joke among Dream World Pokémon is to lead an outsider onto an infinite staircase and watch as they attempt to climb up, only to inevitably get frustrated when they never reach the top.
Entering the Dream World
Whenever a Pokémon sleeps, it's consciousness projects itself into the Dream World for as long as they remain in a dreaming state. When awoken - either via natural or external means - the link to the Dream World is immediately severed and the projected consciousness disappears.
While any Pokémon is capable of making jaunts into the Dream World while they sleep, most of these trips will consist of the Pokémon being at the mercy of the world’s unstable nature. In order to gain any use from the Dream World, a Pokémon must first train itself to take control of the dream before moulding it to a more suitable state. This process has been dubbed as “Lucid Dreaming.”
Many Pokémon choose to enter a Lucid Dreaming state with external help. A common way is to recruit the assistance of a Munna or Mursharna. The odd smoke these Pokémon produce – dubbed by the Scientific community as “Dream Mist” – can allow a Pokémon to more easily enter the Lucid Dreaming state if inhaled whilst they sleep.
Another – more often used method – is for another Pokémon who is either in a Lucid Dreaming state, or a native resident of the Dream World, to seek out the dreaming Pokémon and guide them through their dream until they reach the Lucid Dreaming state.
The third and hardest way is for a Pokémon to train themselves to recognize when they are in a dream, which is almost certain to trigger Lucid Dreaming. Little external help is required, but training to use this method takes time - some Pokémon having an easier time than others. Most budding dreamers seek out help from others instead.
Testing with human subjects using the above methods have all been failures. It was thought impossible for humans to enter until Tagg successfully entered the Dream World, having spent a large amount of time in Pokéform and doing so as a Pokémon first before trying it as a human.
While he was able to switch between human and Pokémon form, he was loath to try roaming around as the former, due to fear of causing panic among the realm's permanent residents.
The only other method of humans accessing the Dream World was during the Dreamstalk incident of mid-2014 to early 2015, in which humans ended up finding themselves in the Dream World in mon form thanks to the Dreamstalk causing a space-time disturbance.
By wresting control of the turbulent reality of the Dream World, a Lucid Dreaming Pokémon will find themselves with the ability to shape the malleable structure of the Dream World to their desire. It’s at this point that almost anything becomes possible for the sleeping Pokémon, as they can perform feats that would be infeasible in the waking world.
However, this great power does have its limits. Try as a Pokémon might, it is impossible for a dreaming Pokémon to harm any fellow dreaming Pokémon in any way whatsoever. It is only merely the consciousness of a Pokémon they’re attacking, and not their physical body.
The worst any Pokémon would be able to do is to try and inflict psychological damage via conjuring nightmarish imagery. However, even this can easily be countered by a Pokémon willingly severing their connection to the Dream World and waking up.
While a Pokémon cannot come to harm in the Dream World, though, if a their projected consciousness is somehow fainted or sustains damage that would be fatal in reality – such as falling from a great height – their link to the Dream World will sever and the sleeping Pokémon will wake up.
Cresselia, the legendary Pokémon of dreams, created the Dream World as a safe place for Pokémon to go while they slept. While it was initially barren, the first dreamers - as they were known - found to their surprise that Pokémon they had dreamed into existence were still there on proceeding visits instead of vanishing upon their conjurer waking up.
Time went on, and a large population of these Pokémon came to be. Left to their own devices, and finding that they had much greater control of the malleable space than their creators in the waking world, the self-dubbed “Dream Pokémon” began to forge a society for themselves.
Dream Pokémon are permanent residents of the Dream World. While a large number keep to themselves, many are happy to interact with visitors from the waking world. This can range from anywhere to consistently visiting a single Pokémon's dreams - Perhaps posing as a guide deliberately giving them bad advice for laughs - all the way to genuine friendships.
Recent times have lead to the latter - at the suggestion of their new friends, most likely - to cross over to the waking world in the form of Pokémon with bodies of solidified Dream Mist.
Otherwise identical to their waking world counterparts, they differ in that upon death a Dream Pokémon will dissolve into its component Dream Mist, leaving no trace of a body. Less grim is their possessing of moves they would not otherwise learn in any other fashion, to a much much higher chance of possessing their species hidden ability.
Large numbers of Dream Pokémon were manifested around the events of Team Plasma's rise, fall, and eventual return in the Unova Region. Manifestations lowered in number shortly before Team Flare's attempted activation of the Ultimate Weapon in the Kalos region. While Dream Pokémon do still cross over to the main universe, it is in much fewer numbers nowadays.
Connection to the Spirit World
The Dream World also connects to the Spirit World, and with the proper knowhow, spirits can be summoned to the Dream World from there, as was the case with Kat's father, who died after getting run over by the Magnet Train.
Spirits of Pokémon who have recently died will manifest in the Dream World. A reaper Pokémon - often a ghost - will turn up shortly to inform them of their death, before guiding them either towards reincarnation or the afterlife.