Here's the breakdown!
나 (na) - I, me, myself
같다 (gat-da) - To be the same, similar
~은 (eun) - makes the verb an adjective describing the word after it
So 나 같은 ____ becomes: A _____ similar to me
Here are some examples to listen to so you can remember it well!
1. 나 같은 여자 (Woman like me)
Listen at 0:51 for the first time they say it! It's part of the chorus :)
2. 나 같은 애 (a youngster like me)
They start saying it at 0:05 and its repeated through the WHOLE SONG hahaha
3. 너 같은 사람 (person like you)
너 means you^^ They start singing at 0:15!