Inferno is an important location in the Bayonetta universe. Created when the cosmos split into three parts, Inferno is the world that houses the universal force of darkness. In the first Bayonetta, it is only talked about and never seen in great detail. In Bayonetta 2, Bayonetta must travel into its depths in order to rescue Jeanne's soul after she is killed by Gomorrah. In both games, both Bayonetta and Jeanne are capable of summoning Inferno's inhabitants to battle against their angelic foes. It's basically the game version of hell.
Inhabitants of Inferno
See list of Infernal Demons.
Bayonetta
Only glimpses are seen of Inferno in the first game, mostly when demons come to claim the bodies of defeated Auditio, when Rodin crosses into the realm when creating weapons for Bayonetta using the golden LPs collected throughout the game, or when the player chooses not to continue on the Game Over screen. It appears only as red, occasionally with twisted deformed hands reaching out or simply bloody in appearance from which screams and other indiscernible noises can be heard.
Bayonetta 2
After Jeanne's soul is dragged into Inferno when trying to protect Bayonetta from a frenzied Gomorrah, Bayonetta vows to rescue her from its clutches. She learns from Rodin and Enzo that the entrance to Inferno, the actual Gates of Hell, resides on the sacred mountain of Fimbulventr that has so far never been found by human hands. Upon arriving in Noatun at the mountain's base, Bayonetta meets the mysterious child Loki who claims that his powers will be needed in order to get to Inferno.
After a long journey and multiple clashes with a masked assailant and a self-titled prophet, Bayonetta eventually finds her way inside Inferno's Seventh Circle. In here, she sees it for what it truly is, a realm where demons run amok free from any control and the very nature of the land is alive with monstrous plant growth and abominations. Inside, she also meets Rodin on a mission to capture a new demonic soul for his new weapon creation and he warns her not to smash up his target to save Jeanne.
Inside an infernal palace of vines, Bayonetta meets the demoness who has claimed Jeanne's soul for her own, Alraune. The demon tells her that there is no real escape from Inferno and battles the witch when she realises who the intruder to her domain is. She is swiftly put down and Bayonetta is able to rescue her friend's soul and eventually gain a new weapon from Rodin at the same time.
Etymology
Inferno in the Bayonetta universe seems to closely mirror the description of Hell found in the poem "The Divine Comedy" by Dante Alighieri. Many of the weapons' backstories and the Infernal Demons found within the game's descriptions make mention of specific locations that take their origin from said poem.
For example, Gomorrah and Fury are said to hail from "the demonic wood, Johnson Forest". This could very well be a reference to "The Wood Of The Suicides", located in the Seventh Circle of Hell. It is described here that those who had taken their own lives were encased in wood and reformed; forever damned to be trees that could not even suffer along with the restless dead. This is the second area of Inferno that Bayonetta enters in Chapter X: The Depths, as evidenced by the appearance of Gomorrah in Chapter XII and the Background OST (The Depths: Johnson Forest). Due to Jeanne's death being of her own choice (sacrificing herself for Bayonetta), this is the circle of Inferno she ends up in. Madama Butterfly and Alraune also inhabit this area due to both once being humans who took their own lives. The trees that Bayonetta has to attack in order to reach new areas may in fact be the trees mentioned in Dante's Inferno, as they appear to be sentient.
Another example comes with the Infernal demon Scolopendra, in which the game describes it as hailing from "...Frejentonta, a river of boiling blood in the depths of inferno." This river is also described in the Seventh Circle of Hell. The name given to it by Dante is "Phlegethon"; the river being a place where violent offenders and spillers of blood are sent and submerged to a level corresponding to their guilt. It is often said Alexander The Great exists in this river submerged up to his eyebrows. A bloody river is seen within the Johnson Forest in Bayonetta 2, as Bayonetta rides Diomedes. As both Johnson Forest's and Frejentonta's respective basis are both located in the Seventh Circle of Inferno, and multiple Scolopendra appear at the entrance of the Johnson Forest, it would be safe to guess the river is Frejentonta.
Additionally, the ice skates Odette, used by Bayonetta, and the ice skates used by Jeanne, Karen, are said to contain the soul of a demon witch and a woman, both of whom were banished to the icy hell "Cocytus". In the Divine Comedy, Cocytus is a lake made of frozen tears within the last circle of hell where it is often stated Lucifer himself resides. It's also stated the tears belong to Lucifer and are frozen by the gust of wind generated by his wings.