This Blood Offering Ritual is necessary in order to level up Arnice and increase her stats, since she doesn't level up normally by defeating fiends. Increasing her level also unlocks additional weapon forms and skills. As the ritual implies, you have to offer the required amount of Blood to the altar and complete the level up process.
The ritual is performed in the Altar of Jorth, which is accessible from the elevator. From here, the shrine maiden who looks like Lilysse will assist you in the ritual. Take note that she'll only appear in the altar if you have accumulated enough blood to perform the ritual and level up. After each ritual, you can ask the maiden select questions to help you understand the lore and the story.
The required amount of blood for each level up increases. As you level up, you'll unlock more skills, more weapon forms, and increase Arnice's stats. She'll also obtain a fixed number of skill points for all her skill attributes.