There comes a time when one must take a position that is neither safe, nor politic, nor popular, but he must take it because conscience tells him it is right.

This quote means that sometimes you have to do something even if it isn’t safe, or if it isn’t a popular opinion, or if it isn’t politically favorable. You have to do it because your conscience – your moral code – is telling you that it is the right thing to do. It might be hard and it might not be popular, but you must do it anyway because it is the right thing to do.