Fusion is the physical joining of an individual and their pokemon, creating one being sharing traits from both. It is a process that only seems possible in the Kasei region, as such, most fusions live in Kasei. Fusion is a relatively recent phenomenon and has only been happening for a generation or so.
For fusion to be possible, a person and their pokemon much have a bond, a connection of some sort. Usually this only comes about once the person and their pokemon have known each other for a time and know each other well. In rare instances, fusion can occur during states of extremely high emotion, such as ones lift being in danger. Even if there is not a deep bond, if both person and pokemon are in a heightened state, it is possible for fusion to occur.
There are two types of fusion, temporary and permanent. Temporary, as the name implies, is a fusion that can be undone. The pokemon will become part of the human, but will return when the fusion is undone. This fusion is not as strong as a permanent one. Permanent fusions can not be undone. The pokemon will forever be a part of the human. Some people can still shift between their human and fusion form. There is not a limit to permanent fusion, as one can have multiple pokemon within them and be able to choose the form of any. However, the more pokemon one has in their mind, the more confused ones mind might become.
Fusion is a very subjective experience that differs by individual. For some it's a flash of light, for others it's a slow shifting and others still might fuse in a manner similar to pokemon evolving. Appearance can vary between individuals as well, even though two people might be the same species. However, it seems that fusion requires at least 25% of one of it's participants to be showing, therefore, there are no cases of someone who looks human, but is actually a fusion, or someone who merely has pokemon ears and tail. Those who are practiced at fusing can even choose to vary their form some during temporary fusion, for example, being a male one time and a female another, or being a bit more pokemon when they need to.
Mentally, fusion is as subjective as it is physically. When some people fuse, the human is in control while the pokemon's mind sleeps. In others, the pokemon is in control. For some, they have a voice in their head or their personality is a combination of both. Those who have practiced can allow their pokemon to take control sometimes while they are in control at other times.
Since fusion was discovered, some 'natural fusions' have been born. They are fusions who were born as they are, due to one or more of their parents being a fusion. While it is possible, most natural born fusions do not have a human form. Natural born fusions can, however, fuse with other pokemon and seem to be, biologically, the same as permanent fusions.
Fusion is decided by the 'bond' stat, which is simply there for the sake of the system. In an IC sense, one would not say 'I have a bond of 150', it's just a manifestation of how close a trainer and their pokemon are.
Temporary fusion will be limited by the Trainer Level. This can be seen as the trainer's knowledge and ability in understanding the pokemon that they are fusing with. Therefore fusing with a level 100 pokemon, your final fusion level will depend on your trainer level. If the pokemon is lowered leveled than the trainer level, that level will be used instead. During temporary fusion, the gender of the pokemon will be used, unless your bond is over 250, then you may choose the gender when you fuse. You can pick a different gender each temporary fusion.
During permanent fusion, your trainer's 'battle level' will be used, as the pokemon becomes part of you. The pokemon's experience is added to your own, so you may gain a few levels, but the level of the fusion itself will depend on the trainer and not the fused pokemon. When you permafuse a gender is chosen, that is the gender that the form will be every time you take it. You will be unable to choose genders each time you fuse.