The arch-vile jump is a speedrunning technique that permits the player to jump very high by allowing himself to be hit by the arch-vile's fire attack. When the arch-vile detonates his column of fire, the player is flung up into the air. If the player is moving forward at the moment the column detonates he can use the height imparted to him to make a super jump over walls, large gaps, and through windows that are otherwise unreachable. As the technique is somewhat of an exploit, it was very likely not meant to exist and will often allow the player to access parts of levels that were not meant to be accessed, or it may act as a sequence break and allow the player to skip collecting a key or hitting an otherwise required switch.
The technique is used in speedruns to create shortcuts that reduce the time necessary to complete a level. Some maps require the player to do this in order to access certain items and places, such as in TNT: Evilution MAP11: Storage Facility (to access a megasphere,) and Icarus MAP25: Another Fine Mess (to access a secret.) Notably, it is required to access the secret exit in Requiem MAP15: Last Resort, in Kama Sutra MAP15: Miss Sporty and in Plutonia 2 MAP15: Where Hate Runs Red. This technique was parodied in Wills's Weirdo Bizarre, or: An Acid Trip Through Time MAP07:Liftoff in which the player has to use several arch-viles to get up to the exit, similar to a rocket taking off.
In Heretic, this technique can also be used with the Iron Liches' Tornado Attacks. It is mildly tricky to direct your motion. This technique can be used on "E3M1: The Storehouse" to skip to the exit or obtain the Hellstaff early. E5M3: Quay has a group of Iron Liches who can provide tornadoes that let you jump onto a nearby tower to grab a Phoenix Rod, especially useful during a "pistol start" run.