To fight the good fight is to do the right thing and to try to get others to do the same. It comes from the Christian religion, so it is deeply rooted in morality and evangelism.
Someone who is fighting the good fight is working tirelessly to try and make good choices and help others. This person wants to improve the world around him.
The phrase is not meant to be taken literally, however, as there is no actual fighting taking place. Rather, fighting the good fight is working hard to accomplish one’s goal of bettering humanity.
