Normalizing: when to apply 2NF and 3NF

I am taking college classes in relational databases for half a year now. As an assignment get to normalize data with 1NF, 2NF and 3NF.

I do not find any difficulties making my schema compatible with 1NF. After that I have not managed to find any examples where to apply 2NF and 3NF as well. It feels like I think a bit ahead when I do 1NF.

When I deliver the assignment, all I have done is 1NF to my understanding. And it still is being approved as valid design.

Is this a normal thing to have? At the moment I do not see the use of 2NF and 3NF when all the redundancy is taken away in 1NF already. Your thoughts?