Should point out that what they mean by "events" is user-object events, like mouseovers and such, not social events like dolphin group members attending a concert. This one snippet gives a hint..

=="accomplished by attaching the method call to the particular UI element you want to track. When used this way, all user activity on such elements is calculated and displayed as Events in the Analytics reporting interface.
With ga.js, you would commonly apply Event Tracking to:
Any see more Flash-driven element, like a Flash website, or a Flash Movie player
Embedded AJAX page elements
Page gadgets
File downloads
Load times for data ==========

SO you could add how many times a video has been viewed and use google analytics to do whatever ppl do with GA.

That said, You sure could use this event tracking for really getting into your video presentations and see how they are being viewed by users. One example of tracking how many times a video is paused during play would be helpful for someone presenting tutorials online. Seeing how many times a user pauses a tutorial might help you pad film with pauses for user to perform tasks along with the video, or just know for sure people ARE following along and doing the tasks with the trainer. (mrpowess, this is for you!)

=="We can also get event more detail by giving the event a "label" which in this case would more appropriately be the movie title: myVideoPlayer._trackEvent('Pause','Titanic'); When executed this code will record 1 click of the pause button while the movie "Titanic" was being played."==

I didn't just pull that all out of my hat, swear. I was just on analyticsexperts.com today after looking at GA mods and I don't know a thing about using GA. Sadly their google analytics 101 webinar is 95 bucks. If you do the beta, then you can sell us classes! :D

(edited to offset quotes from my own comments)