The clip is a short presentation by Terry Moore at 2005's TED (Technology Entertainment and Design) conference. Moore runs New York's Radius Foundation, which I could try to explain, but is better described by the company itself: "[seeking] new ways of exploring and understanding dissimilar conceptual systems or paradigms". One of those systems appears to be shoelace-tying, which you've likely been doing wrong your whole life, according to Moore.
The trick is simple -- just go the other way. If you're left-handed, you might already tie your shoes like this. I'm left-handed myself, but I learnt by rote from my parents, who are both right-handed, so I've been tying crappy knots my whole life. Thanks Mum and Dad!*
I could try and describe the exact process in words, by the video does a better job than I could do with text alone.
* I still love you guys.
I bet you thought you knew how to tie your shoes [TheNextWeb]