What is database normalization? Explain 1NF, 2NF, and 3NF with examples.

I'm learning database design and often hear about database normalization and normal forms like 1NF, 2NF, and 3NF. I understand they're used to organize data, but I'm not sure how each normal form works or why they're important.

Can someone explain what database normalization is, the purpose of 1NF, 2NF, and 3NF, and how each one helps reduce data redundancy and improve data integrity? A simple table-based example showing the transformation from one normal form to another would be very helpful.