This phrase does not have a direct English translation.
화이팅 is an extremely common Korean phrase used to cheer someone or a group of people on.
In America, we don’t have such a phrase. When giving support, we usually say something like “Go David!” or “I believe in you David!” In Korean you can just say 화이팅 to someone, and they will understand.
화이팅 is interchangeable with 파이팅.