Souls are the supernatural properties that give a character the ability to feel emotions, develop personalities, and basically exist as a living entity in the first place. Souls in The HV and Dino-Weapon Show are incredibly powerful, housing characters' Elements, personalities, relationships, and give the characters sentience. They also have unique properties depending on whichever character's soul is in question. Souls also have their own abilities, categorized as "Soul Energy." Souls can be either physical containers such as Glue Bunny's SOUL is, or they can be internal and non-tangible structures inside of a character's body.
With souls, characters:
can feel emotions
can use their Elements
can build relationships and develop complex personalities
use Soul Energy
acknowledge the 4th Wall and even interact with it, depending on the character
Without a soul, characters cannot do any of the things listed above. Instead, they can really only interact with other characters in a binary and monotone way, as they are unable to feel love or hate, leading them to a sense of nihilism and meaninglessness. Very few individuals can accept their own soullessness and continue existing, with possibilities being either psychopaths that kill for no reason, objectively-based entities that aimlessly wander around the world, or even entities that may develop "starter souls" as they try to find a greater meaning in life.
Soul Energy is a metaphysical property of souls that allow the user to perform a variety of different things. The most common uses are:
Traveling Dimensions/Universes & Time Travel: Soul are required in order to travel across dimensions and universes, as well as entering different continuities and traveling to the Main Earth universe (our real world). They are also required to naturally travel through time and space, not including time machines that use souls as a power source, whether it is from a living being or by harnessing a soul that has no "host."
Attacking Souls/Using SOUL Attacks: SOUL attacks are what they sound like; attacks that directly target another's SOUL. They use metaphysical energy such as combining Elements and embodying physical representations of emotions that can harm another character's SOUL. One example that uses this is the game Hollow Knight, where SOUL attacks are a primary game mechanic. SOUL attacks may become physical attacks that can annihilate the physical world, but the user already needs to have a strong soul to begin with.
Unleash A "True Form": If a character is able to "revive" themselves after basically dying and coming back, they can use all of their Soul Energy and "awaken" themselves to become their most powerful versions possible. Only one character in fiction may even have the ability to unlock this form, and that character is UXW himself. No one else nether in fiction nor non-fiction even remotely comes close to meeting the criteria needed to use this. Any other versions such as fan-made creations or characters who say "it's easy" or "hard but possible" and can do it are either faking it or are using "Faux-Energy" that claims to be real but is not, resulting in a distorted vision of their own abilities.
There is one other use for Soul Energy, but it may be extremely controversial, so I will not explain it here.
Souls come in nearly infinite possibilities, but they all roughly follow this simplified category chart:
Basic: Basic Souls are the standard SOUL for most living beings, especially for characters who meet the criteria for having a soul but never acknowledge it, mainly because the creators never bothered to discuss that. These are invisible and intangible parts of a person or creature, which roughly work in the same way; being immortal and cannot be tampered with.
Harnessed: Harnessed Souls are SOULs that either have a physical representation or are stored in some way, such as Glue Bunnies' SOULs. They may sometimes be removed from their owner's body and either still function as normal or may allow the user to control the owner into doing their bidding.
There are other soul types, but these are the ones that I can list right now.
There is no truly meaningful difference between spelling soul as "soul" or "SOUL." The latter spelling is used when it feels appropriate, as just using "soul" may be contradictory in some way, shape, or form.
Most, if not all biological creatures such as animals, humans, extraterrestrials, etc. all have souls from the start, including Main Earth humans. Plants may have souls depending on the creator's decisions (this only applies to fiction).