Celestia is the world above the human world and also where the goddesses live. In Celestia, the goddesses never get hungry or tired meaning they are more than likely to be able to stay in their goddess form all the time while here which would also explain why they were able to fight for so many years without stopping.
Neptune, Noire, Blanc, and Vert are all fighting for the title of True Goddess. Due to the battle between the CPUs lasting for so many years, Vert proposes that instead of taking down the person they liked the least they should instead defeat the person who is the most difficult to fight. This suggestion leads to Noire, Blanc, and Vert all teaming up against Neptune and ultimately defeating her which leads to her being dropped down to the world below.
Path To Celestia
Hyperdimension Neptunia Re;Birth1
Celestia doesn't appear in the reboot, Hyperdimension Neptunia mk2, however after obtaining the item "Celestia Bangle" the description quotes Neptune saying "What the heck happened to Celestia?"
Celestia in the original Japanese version of the series is called Heaven.