This is an excellent question and an excellent quote. Cyrano de Bergerac is the story of a great man who is continually judged by his appearance, the most notable feature of which is an extraordinarily protuberant nose. Those who do not know him make fun of him; the shallow woman he loves (Roxane) would never consider him as a lover because he is not beautiful (though she does have an epiphany once it is too late to be acted upon). This is Cyrano's life, and who he is has been shaped by his appearance.
This quote is Cyrano's statement about who he is. When he says he does not "cut a stylish figure" he means he is not fashionably beautiful. When he says he holds "his soul erect," he means what he IS is beautiful. He is a man of his word, a loyal friend, a steadfast lover, a fearless soldier, an artist, an enemy of injustice, and in all ways a man of integrity and good character.
Cyrano is well aware that he lives in a society full of shallow people who will never recognize the beauty of his soul; this quote is a reminder that external beauty is not what matters most.