The Lost Levels is a remake of the game released in Japan as Super Mario Bros 2. It introduces a number of new obstacles into the standard Super Mario Bros. formula, including poisonous mushrooms, wind, reverse warp zones, and of course many tricky jumps. It's difficult enough that Nintendo of America decided to completely re-theme a different game and release that as Super Mario Bros. 2 instead; The Lost Levels is the first time the Japanese sequel was released to the rest of the world.
This TAS uses Mario's brother Luigi. He jumps higher than Mario, but acts slower in many ways. However, the movie is in no way worse than the Mario version - some new creative solutions have been found.
This is a warpless version. For a warped one see  FDS Super Mario Bros. 2 "warps, Luigi" by HappyLee & KFCMARIO in 08:13.77.