What causes the armies of Mordor to march, clearing the way for the hobbits to reach the volcano?

Aragorn’s army marching to the Black Gates causes Mordor’s forces to move away, helping the hobbits reach Mount Doom.

After the Battle of Minas Tirith, Aragorn and the leaders of the West realize that Frodo and Sam are still somewhere in Mordor. They cannot know exactly where the Ring-bearer is or whether the mission will succeed, so they choose a desperate diversion: march openly toward the Black Gate and challenge Sauron’s power.

The strategy is designed to make Sauron believe that the West is mounting a final attack, or that Aragorn may possess the One Ring. Sauron therefore sends his armies toward the Black Gate, drawing troops and attention away from the interior of Mordor. This creates the crucial window in which Frodo and Sam can climb Mount Doom.

The plan is not intended to defeat Sauron through conventional warfare. The Army of the West is vastly outnumbered; its purpose is to hold Sauron’s attention long enough for the Ring to be destroyed. The Black Gate is also called the Morannon.