The notion of shadows is derived from Carl Jung's psychological theories, as is made explicit in some games that make intertextual reference to his work such as Persona 2 and Persona 4 . According to Jung, the shadow is an accompaniment to one's conscious self, the ego. Although the ego is what is conscious it does not encapsulate all of who we are. Shadows for instance are what we would prefer not to acknowledge about ourselves. Thus, in the Persona series the shadows appear malevolent and evil when in actuality they represent the negative aspect of the human psyche not accepted by the self. However, not everything disowned by the conscious self is negative; it could contain any characteristic or potentiality we do not actively develop or choose to avoid.
In the Persona 2 games, "Shadow Side" are the evil twins created by Nyarlathotep.
Persona 3 and FES
The Kirijo Group's discovery of the Shadows' existence and subsequent experiments on manipulating them, ostensibly as a power source and means of time manipulation, resulted in a catastrophic accident at their laboratories, killing hundreds. They have been appearing, due to the Kirijo Group's experiments, during the Dark Hour, a twenty-fifth hour that takes place every midnight, during which the world comes to a stop and humans reflexively contain themselves in coffins, obliviously "playing dead" to protect themselves from the attention of the Shadows. Occasionally, a human will not transmogrify in this manner, and will quickly become prey of the Shadows, having their minds devoured and becoming vegetative. Only those with Personae, even if they can't be successfully summoned, are immune to this effect and can function normally during the Dark Hour.
The bulk of the Shadows dwell in Tartarus, a massive tower that appears during the Dark Hour, right atop Gekkoukan High School, the site of the previous accident. Each Shadow is defined by two characteristics: the body and the mask. The mask represents the Arcana of the Shadow, while the body helps define its name. These two attributes also aid as a visual reminder of an enemy's weaknesses and strengths. However, each full moon after the Main Character's arrival, powerful Shadows belonging to the first twelve major arcana appear and threaten to wreak havoc. The Specialized Extracurricular Execution Squad is formed to combat these enemies. Once they're defeated, a thirteenth Shadow of the Death arcana appears as an ordinary, carefree teenage boy calling himself Ryoji Mochizuki. However, it's his role to call down Nyx, a being who will exterminate all life in response to humanity's self-destructive desires, but his human side is wracked with guilt over this unavoidable fate.
The Old Documents say that the Shadows arise from human emotions. When enough of Shadows were gathered in one place, they fused together and created Nyx Avatar, which set in motion the events which were to lead up to the The Fall. Aegis delayed the Fall by fracturing Death into the 12 Arcana.
The new episode included in Persona 3: FES, "The Answer" (Episode Aegis in the Japenese version) suggests that a Persona is only a Shadow that remains under control of the mind that created it. This is why Persona-users aren't rendered immediately brain-dead by exposure to other Shadows during the Dark Hour. In addition, The Answer showed that some who've had their Personae artificially induced instead became Shadows themselves, when they proved unable to keep control. In confessing his purpose to the members of SEES, Ryoji implied that Nyx is the mother of the Shadows, but this doesn't entirely fit with what is learned of them here. It is likely that the Shadows - generally resentful and pitiful creatures - would want to call down Nyx to end the lives they were born from.
Shadows and Personae in Persona 4 retains the same roles as they did in Persona 3. Those who face their own personal Shadows in the Midnight Channel and can accept them are able to use their power as Persona, and Igor eventually states outright that they are one and the same. However, the world of the Midnight Channel is more likely to be the true home of the Shadows, as they and Personae appear much more easily there than they did during the Dark Hour. The Midnight Channel itself is a world reflecting the collective human heart, so it's probable that Shadows are spawned there as a result of humans trying to shut away the darkest facts of their personalities.