first form normalizations and second form normalization

Hi everyone,
What is the main difference between first form normalizations and second form normalization ?
In my opinion, they are both generated for the same operation which is to prevent redundancy(in other words; duplication of data in several records).
So would you please explain it to me ?

Thanks

Taken from: http://databases.about.com/od/specificproducts/a/normalization.htm

First normal form (1NF) sets the very basic rules for an organized database:

Eliminate duplicative columns from the same table.

Create separate tables for each group of related data and identify each row with a unique column or set of columns (the primary key).