It is important to remember that Shaw himself subtitled this play "A Comedy and a Philosophy," which highlights the importance of philosophy in this play. In particular, the title shows how this play relates to the ideas of Nietzche, and in particular his concept of the "superman," which he used to refer to an individual who is able to suppress his natural passions and desires and dedicate himself solely to intellectual pursuits. The resulting Superman is much more superior to other men because of his or her ability to ignore the goals of his race, which Nietzsche argued were all about natural passions and desires. Shaw took this idea and developed it by suggesting that a Superman could be created if humans who were paragons of intelligence and morality could mate.
In this play therefore there is the possibility that a Superman could be created through the coupling of Jack Tanner, who is intellectually superior, and Ann Whitefield, who is morally superior. In particular, the play explores the need for philosophy in outstanding individuals. Note what is said about the description of a philosophic man:
...[he] seeks in contemplation to discover the inner will of the world, in invention to discover the means of fulfilling that will, and in action that will by the so-discovered means.
What this means is that all humans should dedicate themselves to becoming the best they can to understand their purpose in life. Having done this, they should then do what they can to create the Superman. The play then is philosophical in the way that it takes philosophical ideas from figures such as Nietzsche and explores them in the context of this play, positing the possibility of breeding a so-called superman who would be superior to other humans through his greater intellectual and moral faculties.