First thing's first - there are three of them - the normal forms. I will talk about the first form.
First form essentially means that entity in a table must represent relation, and if it already does - entity already is compliant with the first normal form. First form imposes two conditions for database design to be compliant with it:
- All rows must be unique.
- All values must be atomic.
All rows must be unique This is usually achieved through giving entity a unique Primary Key column. Unique identification of a row makes it different from row with the same values but different primary key. That's how a bag of data is turned to a set - a core database data structure.
All values must be atomic This is achieved through storing exactly one piece of data in a single cell, not an array of data and not a string of different values separated by comma for example.
That's pretty simple, but for a non-native, digesting information from technical books can be pretty hard, so it makes sense to write down everything I learn.