"Jumping" centers on a group of high school students who discover a mysterious phenomenon that allows them to leap through time and space. The protagonist, Haruto, stumbles upon this ability during a routine track practice when he accidentally transports himself to a different location. As he experiments with his newfound power, he learns that others in his school possess similar abilities, each triggered by specific emotional or physical conditions. The group includes Aiko, a reserved but highly intelligent classmate who uses her jumps to explore historical events; Riku, a rebellious athlete who leverages his jumps to escape confrontations; and Yuna, a cheerful artist who visualizes her destinations through sketches before leaping.

The narrative unfolds as the group realizes their jumps are not random but are connected to a larger, unexplained force. They begin to experience visions of a collapsing world, hinting at a catastrophic event tied to their abilities. As they investigate, they uncover a hidden organization manipulating time for its own agenda, seeking to exploit the students' powers to alter the future. The group must navigate the moral complexities of their abilities, deciding whether to use them for personal gain or to prevent the impending disaster.

Tensions rise as internal conflicts emerge within the group, particularly between Haruto and Riku, who clash over the ethical use of their powers. Aiko's growing obsession with altering the past to save a loved one further complicates their mission. The story delves into themes of responsibility, sacrifice, and the consequences of tampering with time, as the characters grapple with the weight of their choices. The series builds toward a climactic confrontation with the organization, forcing the group to unite and confront the true nature of their abilities and the future they are trying to protect.