The Big Jump is a special ability of Hiryu which allows him to clear long distances. Hiryu builds up speed as he walks down any long incline, allowing him to clear longer distances his normal jump can't and cross over large pitfalls.
Given its situational nature, this ability sees limited use during the course of the game. Among the most notable it can be used to jump over Strobaya's room in St. Petersburg, bypassing the boss battle entirely, and is used in Siberia to clear the large pit between the snow mountain-side and the abandoned power plant in the memorable "Big Run" scene.
The Acceleration Jump works in a similar way, allowing Hiryu to jump farther after building up speed by walking down inclines. In this case, Hiryu can jump much higher and longer than his standard jump, letting him reach high platforms as well as clear large pits.
Much like before, this ability is very situational and difficult to use due to the loose jumping physics. It also becomes obsolete once the easier to use "Jump" Trick is unlocked, as it doubles Hiryu's jump height momentarily.