To me, this story is essentially identical to O. Henry's more famous story "The Gift of the Magi." In both, the theme is love and the things that people do out of love.
In this story, Joe and Delia love each other very much. Because of this, they are each willing to do things that they do not really want to do. Each of them is really into their respective types of art. They want to get ahead in those areas.
But they love each other more. Each of them sacrifices their artistic ambitions for the more important goal of pleasing the person they love.
Theme: "A Service of Love" - O. Henry
1. Human Value and Matrimony
O. Henry has brought more than enough from the human value. "A Service of Love" is nothing but the subject of serving man or woman from his/her art's perspective. Both the characters Delia and Joe do not understand mutually do not get the zest out of the marriagebut they bring marriage at the highest summit of the human value where they can justify that love and art work with one soul. That soul is joy of respecting the art of painting or music. They try to make their love and marriage more mature than any one has made before. They are real Romeo and Juliet who have not made Shakespeare upset but alive. They do not conceptualize the love, but they practice it with their best efforts. Both the characters have the real philosophy of life that they do want to enjoy instead of passing it.
2. Marriage and Fixity
Moreover, besides the matter of Human value and love, O. Henry bears to bring the point that the more any couple adjusts with themselves, greater they enjoy it. Joe always fits in what he has to do. Delia very often learns from Joe how to fit in. If a fixation is quite mutual and understandable, then no any service is so hard as art. O. Henry raises the question, can artists check the real value of marriage by knowing that they have to suffer a lot with their art making. Can they live a poetry life or not the poem life? Poetry for the couple is the result of the poem that they named marriage.