Minun = mine, my
Minulle = to me, for me

Hi! Minun is genetive (my) and minulle is allative (to me/for me).

For example: 

Tämä on minun koirani. This is my dog.
Minun vanhempani asuvat Suomessa. My parents live in Finland.

Vanhempani antoivat sen minulle. My parents gave it to me.
Onko se minulle? Is it for me?

I hope this helps!

Thank you  very much