The Triangle Jump allows Hiryu to bounce off walls in order to reach higher places. To perform it, one has to jump against a wall and then press the jump button and the direction opposite to the wall. If done right, Hiryu will perform a jump off the wall at the direction held. This move can be repeated indefinitely If there's another wall nearby. This skill became infamous among players due to how difficult it is to pull off succesfully, thanks to the game's unpredictable jump physics and controls, and for being mandatory to progress but neither explained nor mentioned in-game at any point.
There are few instances in the game where the Triangle Jump can be utilized. The only two instances where it is required to progress are found in Egypt, the second instance requiring two consecutive uses of the jump in order to clear. This ability becomes obsolete shortly afterwards once the "Jump" Trick is unlocked.
This ability to jump off walls is commonly given to lithe ninja archetypes in fighting games, and as such it is part of Hiryu's movelist in the Marvel vs. Capcom series as well as Guy and Zeku's movelists in the Street Fighter series, among many others. The move usually goes by its name in Japanese, Sankaku Tobi (三角飛び).