Heaven and Hell

Heaven (天国) and Hell (地獄) are phases of reality, which are higher and lower realms respectively, explained as being of "different wavelengths", with Heaven of a higher frequency, and Hell of a lower frequency.

Principles
In traditional Abrahamic religious tradition, Heaven is the realm of God and his angels, though its existence is often interchanged with Paradise, or the final resting place of people that are under God's grace. Hell on the other hand, is traditionally the realm where the Devil and his angels are sent to be punished. Moreover, in many traditions, it is also the place where wicked souls are punished for all eternity, and is often interchanged with Sheol, a place that is separate from God, and a separation from God equals suffering.

Angel Fall Arc
It is first mentioned in Toaru Majutsu no Index, that due to the differing nature of the realms, humans of the world can neither detect Heaven nor Hell, even though both of them exist in the exact location, as is its denizens cannot detect each other and their realms. According to Tsuchimikado Motoharu, only when the denizens of those realms go into the realm between Heaven and Hell, which is the physical world of the living, that the denizens can detect each other. Motoharu continues by saying that their very presence in the human world will result in negative effects to the human world, describing it similarly to an object being lit by an infrared light and becoming hot because of it, or when glass vibrates when there is a high frequency sound. This is of course an inherent property of angels.

Magic God Othinus Arc
As Othinus tries to break Touma's will, he realizes that she is not in fact destroying the world again and again, but keeps changing the world’s point of view. She then explains that the world was not pure and untouched to begin with and that Christian, Buddhist, Celtic, Indian, Shinto, Incan, Aztec, Greek, Roman and Norse cultures and their religions have added layer after layer of various phases over the world like thin veils or filters. So besides Heaven and Hell, there also exists the underworld, the Pure Land, Yomi, the abyss, Mount Olympus, the fairy island, Nirai Kanai, Asgard, and many others. The physical world of the living is one viewed as though through various colors of cellophane. By creating new filters and placing them over the world, the world appears to have changed - a task she claims to be lot easier than destroying everything and building it back up every time. She then mentions that a man who names himself “Silver Star” seems to have been attempting to directly tamper with the 'Pure World' beyond all the filters.