Auldrant is the name of the planet--or world--that Tales of the Abyss takes place on.
According to books you can read in the game, the planet is formed from a six-layer vibration strata which is known as the Fon Belt. From this, the fonons that the planet and living beings, such as humans, that live on it are produced and are able to be controlled. People who learned to control the fonons used them to perform Fonic Artes which became the basis for civilization on Auldrant.
The planet itself is the second satellite of the Rem star and has a rotation period of 24 hours. Its orbital period is 765 days for one year. The sole satellite of the planet itself is called Luna.
At the core of the planet, memory particles can be found which are the source of the planet's energy. It's said they're a fragment of the planet's memory. Dr. Southern-Cross in the Dawn Age proposed a system to generate limitless energy using these particles by funneling them through the fon belt and back into the core. This became known as the Planet Storm and is what powers all modern fonic artes and fontech on Auldrant.
While initially there'd only been six known fonon types within the fon belt, there were some fonists--people who used fonic artes--who discovered a seventh type of fonon within the belt. When they studied these discovered fonons further, they found out that they contained the "memories" of the planet from birth to destruction. This discovery threw the political landscape of Auldrant into chaos, however this would eventually lead to the development of the Score.
Upon the discovery of the Score, the world became split into two groups: those who thought the ability to see the future should be taken advantage of, and those who believed that doing so would only lead to disaster. The rift caused by this split eventually escalated into full-fledged war. As the war was raged and the group that believed in viewing the future began to lose, the fonist known as Yulia appeared.
Yulia, who was particularly skilled at reading the future, read the memories contained within the Seventh Fonon and predicted the future for many hundreds of years in advance. With her appearance and the read Score, the situation quickly changed as people began to hold faith in the "unprecedented prosperity" that was read in Yulia's Score. History proceeded to unfold as dictated by the Score after that.