Obviously, when this armor is worn over skin, the wearer will still need to deal with the ballistic impact of the bullet, bomb fragment or knife.
Norman Wagner, the researcher featured in the video, provided some insight in discussing the research in an earlier interview in 2004:
"We would first like to put this material in a soldier's sleeves and pants, areas that aren't protected by ballistic vests but need to remain flexible. We could also use this material for bomb blankets, to cover suspicious packages or unexploded ordnance. Liquid armor could even be applied to jump boots, so that they would stiffen during impact to support Soldiers' ankles."
The concept of liquid armor, armor that was flexible when necessary but which turns rigid upon impact, was explored by science fiction writers long before its appearance as a product.
He was weaponless, but his suit was a kind of defense. No projectile short of a fast meteorite could harm him. Like a silicone plastic, the pressure suit was soft and malleable under gentle pressures, such as walking, but instantly became rigid all over when something struck it...
(Read more about Larry Niven's flexible armor suit)
A more recent reference from sf author Neal Stephenson, from his 1992 novel Snow Crash provides insight into the practical use of such a product, as well as a cool (and trademarkable) name:
Where his body has bony extremities, the suit has sintered armorgel; feels like gritty jello, protects like a stack of telephone books.
(Read more about sintered armorgel)