When Zoro gets serious, he always wear his headband. Where did he get that? How did it become so important to him? Is there any back story about it (Maybe from a movie or something)?
There isn't any meaning or any special scene related to his headband.
According to the Wiki :-
Zoro normally keeps a black bandanna tied around his left bicep and ties it around his head when he is fighting seriously against an opponent.
Atleast till now, nothing has been revealed about his headband. If it resembles something important, Oda Sensei will mention something about it in the future.
For now, we could just consider it as his style of dressing.