I would want to answer this question by examining the character of Kiki in this excellent novel, who is shown to be one of the major characters who changes and develops during the course of the novel. In paricular, we see her change and grow in terms of her own love and acceptance of herself through her friendship with Carlene Kipps, who seems to instill Kiki with greater self-respect and love than she had before. This is of course crucial for Kiki in the situation that she finds herself in. Married to a cheating and deceiving husband, she has already clearly stated to him that she will not have any further relations with him, but they continue to live together.
It is through her friendship with Carlene, therefore, that Kiki finds the strength to live her life pursuing her own desires and wants rather than laying these down for the happiness of others, such as her children and husband. The sacrificial gift of the priceless painting she receives from Carlene after her death is something that therefore liberates Kiki to act on those desires and to live the life thatshe wanted. However, she is only able to do this because she has come to love herself, freeing her to love others.