Enrico Pucci was a fanatical disciple of DIO, an ancient and immensely powerful vampire. Before DIO's destruction in 1989, he shared with Pucci a philosophical concept for achieving "Heaven." This was not a religious afterlife, but a state of absolute, deterministic peace for all of humanity.
To achieve "Heaven," every living soul needed to inherently know their entire destiny, allowing them to accept their fate without despair.
This required a universe-wide temporal acceleration to force all souls to experience the full timeline of existence, from beginning to end, before looping back into a new universe.
DIO inscribed the exact ritualistic steps to achieve this in a notebook, which was subsequently destroyed by Jotaro Kujo. Pucci dedicated his life to extracting those memories from Jotaro to execute the plan.