I remember running into that site when I first waded into tables. It's nice.
For complex data tables, you must use newer accessibility tags such as SCOPE, CAPTION, SUMMARY, ABBR, ACRONYM, TFOOT and THEAD as needed to further organize information in complex data tables.
I don't know why, but it doesn't mention "headers" attribute (I know these are mostly tags listed but then there's summary!). Headers is pretty much what you use if your table is "complex" (not every data cell match the row to their left or their column above). This is often when single data cells belong under more than one category. I use headers, though likely it's my bad table-writing skills since everyone says it's rather rare to use them.
A read an argument-- er, discussion about HTML where some people pointed out that scope isn't available to all popular screen readers, but I don't know who those are. JAWS knows scope, headers, and even axis! Which I didn't know but think is way cool (3-d tables, or database-style table searching... neat).