[upofadown]

It is where you fly the aircraft sideways through the air.

It is a way of dealing with the situation where the wind is not coming straight down the runway while landing a light power aircraft. You point the aircraft straight down the runway and add in enough bank to overcome the drift to the side. You use the rudders to prevent the aircraft from turning due to the bank.

Pearson was performing the forward-slip in the less common context of gliding. While flying gliders the problem is that they produce a glide angle that is much too shallow to ever be able to control exactly where you are going to land. Normally you use spoilers (AKA dive brakes) to control glide angle but the spoilers might fail or you might need a steeper approach angle than the spoilers can provide. So you fly sideways to force the side of the glider through the air and produce more drag. You still need to take into account any crosswind while simultaneously adjusting the glide angle while staying lined up with the runway. It's a bit tricky and it takes some practice to maintain the skill. That's why I get to demonstrate a forward-slip as part of my yearly glider check flights.

Pearson did this in an airliner with constantly changing control forces and completely nailed it on his first try. He touched down something like 100 feet past the threshold which is exactly what you want to do in a case where you don't have a lot of braking available. This was one of those times where you wanted the guy that lives aviation and not the nine to fiver.