Sun Pillars

The definition is correct. However, what the video showed were not sun pillars, they were crepuscular rays. That's a fancy name for the rays that come from the Sun as it sets. You've probably seen them; the clouds break the sunlight up into beams of light, and due to perspective (the same effect that makes railroad tracks appear to converge in the distance) they look like they fan out from the Sun. Anytime there are high clouds or hazy skies you can usually see them, although they can be very faint. If you're very lucky, the rays can go clear across the sky, and because of perspective again they appear to converge once more at the point in the sky opposite the Sun. If you want to impress your friends you can casually comment, "Oh yes, those are just crepuscular rays converging at the anti-solar apex". ;-)

A sun pillar, on the other hand, is a vertical column of light that comes up from the setting sun. It is caused by ice crystals that reflect the light of the Sun back to the observer. It's pretty common to see them in the winter. The big difference here is that pillars are vertical, while crepuscular rays spread out in all directions. They're both pretty though.

The excellent web site WW2010 at the University of Illinois has great pages about both sun pillars and crepuscular rays, as well as lots of other atmospheric phenomena, complete with great pictures and diagrams. Highly Recommended!