Spiritual energy is a kind of life force tied to humans in the Path to Nowhere universe. It can be likened to qi or mana: an invisible, intangible essence that normally has no effect on the external world. In fact, despite every human being "possessing" spiritual energy, it is stated to exist outside of the "physical dimension" in an alternate dimension of its own. While it seems that every person serves as a link between these two dimensions, spiritual energy cannot cross into the physical dimension without the involvement of a force like Mania. When this does occur, the consequences are dire, warping the nature of reality itself.
Spiritual Contamination
Spiritual contamination, also referred to as mental contamination, is what results from spiritual energy being forced out of the spiritual dimension and into the physical one. Contamination and corruption are not substances that exist independently of this process, but are exclusively a byproduct of it, as if they were liquid runoff from a solid (in this case, the energy) being pushed through a fine mesh strainer (the border between dimensions). Mania has no inherent corrupting properties beyond forcing this process to occur. Ambrosia performs a similar role, purging negative emotions from a person's dream and creating a dark, viscous substance that assumes a physical, semi-sentient humanoid form.
Given that Sinners draw their power from Mania, their abilities likely also operate on a similar principle. In experiencing an acute emotion that strongly affects their overall being, Sinners gain the ability to focus their spiritual energy through a means tied to the original trigger of their awakening. Unlike Maniacs who experience a wide range of negative emotions throughout their transformation, this singular emotion seems to create a kind of pathway that allows the energy to flow more freely, though not entirely without consequence. As shown, Sinners' M-Values still increase when they use their powers, and more generalized negative emotions can still worsen their corruption state.
The Shackles seem to at least partially function like Sinner abilities, especially when the Chief uses them as a weapon, projecting red spikes with a similar color to Mania Crystals. The aspect of the Shackles that Earl refers to as "the Forbidden Force" could also be an example of this, as it allows the Chief to use their internal thoughts to alter the external world, though as the Phantom Hamel points out, this bears a close resemblance to the way a Corpus controls the denizens of its Black Ring.
Spiritual Realm
A spiritual realm is the name given to how a person's interior thoughts can create a kind of pseudo three-dimensional space within the Deep Mania, where the mind can affect the fabric of the imagined reality. Dreams, Mirages, and mental labyrinths are all examples of this, as while they aren't "places" that exist in a physical sense, the Chief and others can consciously move through and interact with them as though they were. Notably, the Chief is incapable of dreaming, which implies that they may lack something fundamental with regards to spiritual energy.
Black Rings are the one exception to the metaphysicality of spiritual realms, as they're created in reality instead of in the mind. Beyond that, however, they function in much the same way. A Black Ring can be likened to more of a lucid dream: instead of simply being part of what happens within it, its Corpus has absolute control of all things inside of it, giving them the ability to defy the laws of physics and reshape space in a way that wouldn't normally be possible without following a sort of "dream logic". This causes a great risk to those trapped inside of it, as they risk their consciousness being overridden by the contamination caused by the Host. In a sense, this process would change them from a "real" individual to an image of them that might appear in another's dream -- they would become a part of the Corpus's vision of reality instead of their own, and since Mania is the driving force behind this process, they become a Corruptor instead of staying human. This effectively renders them a puppet that can only follow the Host's will.
Ambrosia offers an alternative path to achieving this level of control over one's own spiritual realm, but it is limited to the metaphysical space of dreams.
Some S-Rank Sinners, such as Etti, are capable of creating spiritual realms at will. In other cases, such as Eleven, a deteriorated mental state can result in the creation of one, the high concentration of Mania resonating with its source.
Ring Substance
Much like standard spiritual contamination requires a source of spiritual energy to form, the Ring substance draws its energy directly from otherworldly entities, only able to do so when a strong enough connection with one is present, such as within a Black Ring or via an Inheritance. The Ring substance possesses the ability to "resonate" with Sinners, mirroring the output of energy from their Manic state and condensing to form Mania Crystals. Summer describes it as containing "extreme mental power," using it to directly power her Ring Weapon. Given its volatility, Mania Crystals are slightly more reliable as a power source.
Summer also refers to the Ring substance as "a blank catalyst which only amplifies and catalyzes to others' wills."