3rd normal form??
It is about the steps you take to "clean" your database ideas - the 5 housekeeping checks to get a "clean" database. They're more mathematical than that.
IIRC the 1st normal form is about not having repeating columns and having an unique key (single or composite) in each table
the second normal form is about splitting off things that belong together into separate related tables (i.e. taking the product information outside of the shopping cart or separating address from personal details), making sure all your information is directly related to the key. This is about breaking down your content and index into meanigful data sub-chunks
The 3rd normal form is that the data in my table that actually exists "outside" this table's context should be outside it, this is where it really gets relational. Here you hunt down columns that dont belong in one table but should be separated...
Theres a few more steps after that that get more and more mathematical
Once you reach your clean database you often have to start "breaking" the cleanness for performance reason, using views or cache tables etc.
I'm sure people taking courses at the moment have it clearer in their head.