"Karagöz" means black eye and it root contain from kara (black) + göz (eye) and "Karagözlüm" means my one with black eyes 

Also"Karagöz" is a character of the traditional Turkish shadow play which is also using by Eyptian Arabs in the shadow play under كراكوز name 

Bana yardım edin ,,Help please

please guys can anyone tell me what does "Karagöz" or probably "Karagözlüm" mean ?
and what are the roots of that expression ?

"Karagöz" is a kind of traditional "shadow play" ( gölge oyunu ) The name of play is Karagöz. 

In this game there are two stars (person) as "Karagöz" and "Hacivat"

And the other character as "Tuzsuz Deli Bekir, Bebe Ruhi, etc..."

There are comic dialogs between Karagöz and Hacivat (But to understand these dialogs  you need a good Turkish because the comics based on "word misunderstanding"

It is called that Karagöz and Hacivat were real characters who lived in the time of Orhan Ghazi the second emperor of Ottomans ( For more information just check google )

"Karagözüm"... Hacivat call to his friend Karagöz as Karagözüm... It is a sign that they are so closed friendship...

You can find so many informations and also pictures from google...