In The Awakening, the protagonist Edna Pontellier leads a life that does not make her entirely happy. She is married and has children which conforms to the standard social conventions of Edna's time. However, she inwardly questions whether or not she should try to break free from this life to find her own independence and happiness. While she goes through the motions in her everyday life, Edna continually questions whether or not it is right for society to force her (and other women) into such a narrow lifestyle. Soon Edna begins to neglect her children and she has a love affair with another man, proving that her inner questioning gets the better of her and motivates to seek a new lifestyle.
In Kate Chopin's The Awakening, the "outward life" mentioned in this passage refers to the moralistic set of narrowed expectations that phallocentric society imposes upon women, whereas the "inward life which questions" addresses the protagonist Edna's resolve against these restrictive standards. Initially, Edna leads a normative feminine experience, fulfilling her expected roles as a wife and mother. While she participates in these roles, she yearns for freedom and independence from these reductive norms.
As the novel progresses, Edna revolts against the patriarchal conventions of the time. Her actions start out subtly when she refuses to participate as a host, and escalate to her moving out of her husband's house and engaging in a physical affair. She eschews her prescribed gender duties, disregarding her maternal obligations and instead choosing to lead an independent life. Her refusal to ascribe to the gender norms of the time ostracizes her, and Chopin ends the novel on a dark note by having Edna commit suicide. This shows the oppression that women faced at the time as the detrimental force it truly was.