This is a tool-assisted speedrun, made on an emulator, using frame-by-frame shooting, savestates, and rerecords to overcome reaction time and human error. As such, it is purely a form of entertainment, and is not designed to show skill.
Mario has eaten too many poisonous mushrooms and as a result, decided to go on a furious killing spree. In this berserker state he has also gained the new secret ability to walk through walls at will.
Wondering how some tricks work? Information is available at Super Mario Bros. Tricks page.
This version is really faster than the previous on some levels, but emulator differences (specifically Famtasia's faster loading time) balances out the time.
This is the real Super Mario Bros 2. It was never officially released in the USA and Europe. It was later ported to SNES, and released as "Lost Levels" on Super Mario All-stars. Phil remembers there were pirate copies of this game under the name Super Mario Bros. 3.
FDS means Famicom Disk System. It was a Japanese disk-unit version of the NES.