yeah, so a barber chair usually happens when the tree being cut is under a lot of tension, and is more likely to happen when a living tree is being cut when it has its leaves and especially if the tree is leaning - so basically, and time there is tension being put on the tree in one direction. Then, if you cut into the tree, instead of the wood holding until you cut through enough of it for the tree to fall over, a section of the trunk lets loose and springs up in the air.
that video was a super extreme version I guess and not the best for illustration because the whole tree basically flew apart - that I don't think is typical of a 'regular' barber chair.
its hard to explain without an illustration.
when you cut a tree, you first cut a notch on the side of the trunk that you want the tree to fall. then you go to the opposite side of the tree and make a perfectly straight flat cut towards the notch - that's called the back cut. If there is a lot of tension in the trunk to where the tree is really leaning towards the notch side of the tree already - when you make the back cut, a piece of the trunk can let loose and spring up in the air, which is obviously super dangerous, because if you are standing back there you can get hit with an unbelievable amount of force, and fast.
certain species of trees are more likely to barber chair, and again, more likely when they are green or have leaves, or if the tree is full of snow or ice or if its windy or heavily leaning or something like that.
and again, usually the whole tree doesn't implode like in the video. usually just a strip splits and pops up from the back.
there are techniques to help reduce the chances if the tree seems like it might barber chair - like instead of a full back cut, you could do a plunge cut towards the notch - leaving a strap of wood on the back - and then the final back cut is done just above the plunge. if course you couldn't do that on a tree as big as the one in the video.