The Tower is a set of circular ruins situated below the forested cliff housing the Academy. It is one of the shrines located on academy grounds.
The Tower was first referenced by Irina, when Guillaume informed her of the ceremony Captain Fukayama planned to perform in the school. This would undo the "change in time", and presumably ruin the Truants' mission. Despite Vanessa's objections, Irina claimed that this won't alter their plans—just that they needed to get there sooner.
After walking for about a mile, Irina, Ian, Guillaume, Vanessa, Hisao, and Hunter reach the Tower. It was abandoned, and parts of the forest have begun growing on the ruins. As the party moved towards the Tower base, Irina reminded them to strategize in advance—once inside, they won't be able to understand each other.
The team began ascending the Tower via its circular steps after a pre-arranged signal flare lit the sky above the Academy. Upon reaching the top, the students are teleported back in time—to an age where the Temple was intact and in use. Irina's warning proved prescient, as each student was now speaking in a different language. Their intrusion did not alarm the priest officiating the ritual; in fact, he was expecting them.
Despite the language barrier, the students began carrying out their assigned roles. The ritual was interrupted when Jun saw an image of his twin appear as the sacrifice. Disgusted with what he learned, he shouted at Hunter, telling him to run. Hunter obliged, and ran back the way he came from. Irina's rifle shot hit him in the right shoulder, but he managed to escape the Temple and return back to the future.
The Tower references the Tower of Babel described in the Bible, in Genesis 11:1-9. In this story, the world had a common language. A group of people in Babylon decided to build a tower that reaches into the heavens. To stop them, the Lord confused the language of the entire world, and they stopped building the tower. Babel sounds like the Hebrew world for "confused".
A Sumerian parallel to the Genesis account exists, called Enmerkar and the Lord of Aratta. In this story, Enmerkar, king of Uruk, built a massive ziggurat (temple) to the goddess Inanna. At one point, he beseeched the god Enki to unify the languages of the world, so that they may worship in a single language.