Shadows are the monsters of the Persona series that can take forms of a person's deepest resentments or wishes.
Shadows in the Persona series are a term used to describe the creatures that lurk inside the "dungeons" that the characters enter, they are the deep dark thoughts of the human mind. Shadows in their original form are represented as blobs of darkness with mask on, and when engaged they take on the form of these thoughts that created them. Smaller shadows come together to form into larger stronger shadows. There have been various other incarnations of shadows, for example in the Persona 4 series there are shadows that are created by the negative thoughts of specific characters who are thrown into the television which represent the hidden secrets that person possesses. When that person rejects the shadow it goes berserk and lashes out, transforming into something stronger and more deadly.
Shadows first appeared in the manga/anime community in the Persona 3 manga. In this they would come to life during a hidden hour in time when people with limited perception would be trapped, frozen and unaware that the time was passing. They would then come out and hunt down anyone with heightened perception and slay them during this time. They lived inside a castle called Tartarus that appeared during the Midnight Hour and it was the job of SEES, a group of Persona users, to hunt them down.
In Persona 4, Shadows were once again representations of the inner demons of the human mind, and this time they existed inside The Midnight Channel, a world inside the Television. Teddy explains to people that shadows were always there and that whenever the fog inside the Midnight Channel clears (meaning it gets foggy in the real world) they go crazy and start attacking anyone they can find.
These are the common enemies that live inside the Midnight Channel and Tartarus. They are the living embodiments of the dark and hidden parts of the human psyche, the bad thoughts we repress. They can take on numerous forms to represent these beliefs, appearing as anything from babies with flowers growing from their brains, to birds holding lanterns, to even police officers and royalty.
Once enough Lesser Shadows come together, they merge into one larger much more powerful creature. In the game these shadows are typically mid-bosses on levels.
In Persona 3, there are shadows that appear on full moons and are fragments Death itself. They were shattered off when Thanatos was sealed inside the hero of the series. Each one of these shadows represent the different tarot card that it was named after, such as "The Lovers" or "Emperor."
In Persona 4, when a person is thought of enough, that person appears on a television screen that is turned off during a rain storm. If that person is then thrown into the television, then they're inner most thoughts and deepest secrets come out and take form as their own Shadow, which is the representation of what they want to hide about themselves. If this person accepts that the shadow is a part of them, then the shadow fades back into them and becomes a Persona for them to use. If they reject the shadow, then it goes into a state of rage and transforms into it's true form.
Yosuke's shadow appears before him and Souji and reveals that he hates living in Inaba and thinks everything in this dinky little town sucks. Yosuke rejects the shadow and it transforms into a giant frog with a scarfed ninja sitting on it's head.
Yukiko's shadow tells her friends that she hates being the child of the town's Inn and wants her "prince" to come rescue her. Because of this she resides inside of a castle and dresses like a princess. When rejected she turns into a giant red bird with Yukiko's face.
Chie's shadow appears inside Yukiko's castle when Chie is trying to rescue her friend, and says that Chie gets off on the idea of making Yukiko feel dependent upon her, oh making someone so pretty and popular feel beneath her. When rejected the shadow turns into a dominatrix that sits atop a tower of mindless school girls.
Kanji's shadow appears in a bathhouse dressed in just a small towel and reveals that he just wants to be accepted and that he is afraid of girls, and that he thinks men are far easier to understand. When rejected he transforms into a giant surrounded by roses.
Rise, being a pop star who wants to run away from that life, has her shadow appear in a bikini and is the bubbly ditzy incarnation of her pop idol persona that she hates to admit is actually a part of herself. When rejected it transforms into a stripper with a satellite disk for a face.
Naoto, having grown up far too fast, has a shadow that acts childish and pretends to be a mad scientist. When rejected it transforms into a giant toy robot.
Teddy longs to know what he really is, so when he fears that he might be nothing his shadow appears as an empty soulless void of himself. When rejected it grows into a larger decaying version of it's original form.