oppa(오빠) means "an older brother", and it is only used when a girl is calling an older brother or a older man who she trusts.
In English, you can call someone brother (or sister) to show that you are a close friend.
But in Korean, when a girl call a man "oppa" , it implies that she regards him as an older brother who usually takes care of everything about her like her parents.
In Korean culture, an older brother has a similar role to parents who take care of family. So, when a girl call a man "oppa", it implies that she trust him like she trusts her parents, and also it implies that she allows him to take care of her as her parents are doing to her.
When a girl call a man oppa, it is supposed that she regards that he is in a position to treat her a meal, and you can see such a scene in Korean movies and dramas. Also, when a girl is calling a man "oppa", he feels that he can get closer to her easilly.
Because of this cultural background, "oppa" is used by a girl when she wants to express her good feeling toward a man, and often Korean female fans call a male celebrity "oppa".