Colin, web validation just ensures that the page conforms to web standards. Most browsers can make up for it, but it's good to have.
http://validator.w3.org/ will tell you whats wrong.
Nested tables is a method for laying out web pages that is largely considered to be a bit old and clumsy as there's much better ways of doing it, but for the amateur it's easier to do tables. Hell, for me it's often easier!
If you can think of structuring a page using cells in excel by adjusting their sizes etc. then you can maybe picture how it works.