Once you have your tables in 1NF you are ready for the next step:
A 'technical' definition of 2NF:
'unique identifier' is mentioned in both conditions. Let's take a closer look.
The goal of 2NF is to eliminate partial dependencies. And of course those are when an attribute that is NOT part of a key, depends on only PART of a composite key (one or more columns used as key), instead of the complete key.
For example, in a database of employees, the employee ID number may partially determine the employee's address, but not the employee's name or other personal information.