The arcane art of Demon Summoning are based around the principle of making contracts with various different demons. These contracts offer boons and service in return for her giving offerings at specific times in specific ways. These contracts must be fulfilled, even if she is in mid-battle, or the demons will consume parts of her body or soul.
As this suggests Demon Summoning is an extremely dangerous form of magic and most users end up dead due to its use. However if the user is careful about what contracts they make and meticulous in their upkeep of those contracts they can gain extremely powerful allies.
Kazumi's Phoenix tattoo is the representation of her contract with the Phoenix demon known as Arthur. The deal made between the two of them is that Arthur is her to protect her from physical harm.
Kazumi's Raiju is in the form of a cat with the power of thunder and lightning.