Sprint shoes are a relic that any character can equip. With sprint shoes equipped, the walking speed of the on-screen character is doubled.
The initial release of Final Fantasy 6 (Final Fantasy 3 outside Japan) did not have a mechanic where the player could press and hold a button to run. Sprint Shoes were therefore arguably the most important item in the game.
Future remakes included the button sprint mechanic. With the button and the sprint shoes equipped, players could run at quadruple the default walking speed, which was never originally intended.