Most of the information given here is taken from the VS Battles wiki so please give the members of the VS Battles wiki (especially the Admins) the credit they most definitely deserve.
The ability defined as the power to be supremely almighty and invincible, in every sense and aspect.
It is also sometimes called "Unlimited Power," Characters which are omnipotent can literally do anything as they are considered the be-all and end-all of characters and most of the time, God. They would by default be absolute strongest beings in their respective fictional franchises.
The user would be capable of achieving absolutely anything without any limit or condition, including that which is conceptually impossible, such as "having power exceeding infinity."
Its one and only wielder is and will always be fundamentally and absolutely invincible, completely immune to all other powers. They are boundlessly above absolutely everything, including existence and nonexistence, all duality, trans duality, life, death, possibility, and causality and are capable of erasing the combined might of all Creation and its mightiest beings with just a mere thought and simply restore everything in the exact same manner.
In fiction characters can only be presumably omnipotent, as much like in theology it is impossible to prove. This is best defined by what is know as the "Omnipotence Paradox".
The Omnipotence Paradox states that "If a being can perform any action, then it should be able to create a task that it is unable to perform. Hence, this being cannot perform all actions. On the other hand, if this being cannot create a task that it is unable to perform, then there is something it cannot do"
Also according to the dictionary definition, omnipotence could simply mean "infinite in power" or "having very great or unlimited authority or power", meaning a term defining its standing in relation to a certain setting and its inhabitants.
However, given the highly logically self-contradictory nature of the "can do anything whatsoever" definition of omnipotence (see the above image for an example) within this Wiki (much like the main VS Battles), even characters with the highest "0" ranking are only described as having "Questionable Omnipotence".
In additio if an author simply mentions the word "omnipotence", this is obviously not enough to justify that some character remotely fulfills the requirements for tier 0. Because the understanding of different authors can be very different, and the author should also make clear that the entity is totally qualitatively superior to everything else. Completely unlimited, not just playing on the same field as other powerful beings from that fictional verse.
For more in-depth information, please read this.
In the Kabbalistic system there is a thing (God or one of the attributes of God) called Ain Soph. It means boundlessness.
This is a strictly philosophical and theological term. There are not important feats or bulky descriptions about superiority over logic (or anything else).
It is just an attempt to create a model of an Absolute God. It is boundlessness beyond all perspectives or any other concepts. Any description (including any words that we may provide here) will be limited.
Transcendence, increased scale, multiplication by infinity, or any other option is meaningless. Boundlessness already includes all of those actions and is still boundless compared with any such options in any way.
But in addition to Ain Soph there is also Ain. Absolutely "nothing". Not even boundlessness, not everything, not nothing, just "not". You can not say or think anything about Ain (any words and thoughts are limited), you can only keep silent about Ain.
The other major theological systems (Christianity, Islam, Buddhism, Hinduism) also have similar concepts.
Or to put it in simpler terms: Omnipotence has no relation to something like "A character just destroyed 1,000,000 Omniverses".
In addition, a real life author (living within our reality) should logically not be considered a character within fiction in any sense.
For example, the fictional character Superman will exist no matter how many comics that somebody destroys, or if you somebody "defeats" the author. No matter how many fanfiction stories about the death of Superman that are written, or even if the official authors decide to kill him in their works, this fictional character will likely continue to exist even after your and said authors' deaths.
To use another example, The Lord of Nightmares beat her "author" with a shovel, but this does not really mean anything. The fourth wall is a meaningless nonsensical concept. This only happened as a part of fiction, and it does not affect reality in any way.