The Cauldron is the Azure Grimoire's original form. Its purpose is to gather souls to smelt the sword in its body.
The 13th Prime Field Device, Nu-13, was tempered at the bottom of the Kagutsuchi branch office. The Murakumo Unit, in order to be complete, needed the other grimoire, which Ragna the Bloodedge had. When Ragna and Nu fell into the cauldron and were smelted together, something went wrong and resulted in the Black Beast, a failed experiment, being created. Mu-12 embodied the true Azure, and became the perfect Murakumo Unit, Kusanagi.
Similarly to a Nox Nyctores, it takes thousands of souls to create a Murakumo Unit, which explains why the Kagutsuchi NOL branch was completely empty in most stories in Calamity Trigger. Hazama had sacrificed the NOL soldiers inside the branch so both Mu-12 and Nu-13 could be smelted. Judging by most endings besides being able to create the perfect Murakumo Unit, the cauldron has the power to send a being into the past by 100 years or more as shown with Nu, Ragna and Jin.
The Cauldron can also kill somebody by mostly reducing their body to almost nothing by sending them into the Boundary as seen with Nu in Calamity Trigger's true ending (Although, by the end of Continuum Shift's true ending, it is shown that Nu's body had the ability to regenerate itself). Mu-12's cauldron is located at the top of the NOL branch of Kagutsuchi, while Nu-13's is located at the bottom.