An Auto-Jump is a game mechanic from multiple games in The Legend of Zelda series.
By contrast, in 3D games beginning with Ocarina of Time but not including Breath of the Wild, an auto-jump is performed whenever Link approaches an unobstructed ledge with enough speed. Rather than simply fall off the ledge, he will automatically leap from it, allowing him to cross short gaps.
By making the jumping action automatic, an extra button in the control scheme can be allocated to other actions such as using items. The Adventure of Link was the only main Zelda game to have a button dedicated to jumping until Breath of the Wild, which discarded the auto-jump as a primary mechanic.