Since my earlier reply, I read through the Technical Explanation, and I did find it a lot more helpful than the Intuitive Explanation. The latter did a good job of explaining the theorem, but the former more clearly enunciated why anyone but a statistician should care.

Also--following up on my previous comment--someone asked after the longer post describing my experience with the sequences and my suggestions for easier integration of newbies, so I pasted it over here for anyone interested. I recommend reading that in addition to the thread I already linked, not instead of; most of the thread took place after I wrote it.