Cool man...Fibonacci Numbers as explained by Ken Nordine...

This is by Ken Nordine of WordJazz.com. It's actually a pretty good explanation of it, even though he's not a math expert. He's a "voice" guy who you have probably heard on commercials over the years - such as Levi's or Natural Gas.

Now - for the educational stuff! 

See this excellent video on the Fibonacci Sequence which explains the history and - most importantly - what makes it useful.  There is also an explanation of  the golden ratio, golden triangle, golden rectangle - all of the "golden" proportions.   This is also a pretty good video by TeacherTube about the golden ratio.

For some reading on the subject, see the most comprehensive web site about Fibonacci numbers that I have found on the web at Fibonacci Numbers and the Golden Section - this is the site of Dr. Ron Knott which includes multimedia presentations suitable for everyone.  This is an excellent web site with many hyperlinks and so much material that it would keep any interested upper elementary or middle/high schooler busy for many hours.  If your child is especially interested in mathematics - or you just wish they were (lol!) - you might want to introduce them to interesting math-y topics like this.

I can't talk about Fibonacci numbers without talking about the Penrose the Mathematical Cat books, in which mathematical concepts - like Fibonacci numbers - are introduced in the form of a story about a cat named Penrose and his adventures.

Related:  Fibonacci numbers in nature