There are a few different ways to shift Mario the required 20-30 pixels to the right for this trick to work.
The most popular method is with a "Backwards Bump". Mario's on-screen position changes by several pixels anytime he brushes a wall while jumping backwards - He moves ahead slightly further than the screen scrolls.
As long as Mario is still shifted to the right when he enters the pipe, he'll go directly to the above-ground Warp Zone area.
(The glitch even works in the Super Mario All-Stars version)
The ability to skip past the vine and onto Warp Zone saves precious seconds for speed runs. It's also really neat to learn what's happening behind the scenes... The first video features the evolution of all fastest known routes leading up to and including the discovery of "Wrong Warp". The other clips specifically discuss the World 4-2 Wrong Warp glitch:
4-2: The History of Super Mario Bros.' Most Infamous Level (20 min, 30 sec) by Summoning Salt
Darbian explains Wrong-Warp (3:23)
SMB1 4-2 wrong warp tutorial/explanation (3:44) by andrewg1990