Now if the function of man is an activity of soul which follows or implies a rational principle, and if we say ‘so-and-so-and ‘a good so-and-so’ have a function which is the same in kind, e.g., a lyre, and a good lyre-player, and so without qualification in all cases, eminence in respect of goodness being idded to the name of the function (for the function of a lyre-player is to play the lyre, and that of a good lyre-player is to do so well): if this is the case, and we state the function of man to be a certain kind of life, and this is to be an activity or actions of the soul implying a rational principle, and the function of a good man is to be the good and noble performance of these
What he is saying is basically that humans differ from other animals in that they have an ability of complex reasoning and, therefore, in order to fulfill their purpose, they need to excel at reasoning "in accordance with virtue". I'm not sure whether he already includes that in the "rational principle", but I think I would also include the ability for introspection as one of the distinguishing capabilities of humans that they have to utilize to reach their potential. Because if we were incapable to reflect on our past reasoning, we wouldn't be able to become better.