Much thanks to David Fisher for posting this clever demonstration about how soap works. David is a DFW area soaper who writes the Candle and Soap Making forum on About.com.
Demo: How Soap Cleans
For a more scientific explanation, take a look at the chemistry forum on the About.com site:
The Chemistry of How Soap Cleans
This is a great explanation, but David's demo has better pictures!
Enjoy your day!