The entire novel follows the life of Clara, but we are introduced to her life through the men in it. Each of the three chronological parts of the novel should be considered somewhat distinct. Each has its own point of view, and its own protagonist.
This triptych structure follows the structure of The Garden of Earthly Delights, a triptych painting by Hieronymus Bosch (see image under). The painting's panels are each distinct, but each important to the whole story when read from left to right.
The work is an investigation into the American class system, and the characterization of poverty. Clara spends her whole life seeking freedom, independence, and an escape from her poverty stricken, violent past. She is literally born in a ditch on the side of the road. But in the end, her son is gripped by the same all-consuming burden: to escape from the cycle of poverty.
Highlighted within this struggle is the nature of relationships, especially that of mother and child. Sometimes the relationship is one of sole duty and care, and sometimes characters act more like husband and wife (sharing their life together). Some of Clara's relationships take on a father-daughter feel, where freedoms are limited.
All the characters are seeking to grow, both personally and through the class system. Swan (Clara's son) isn't the only one trapped by his past (or even his parents' past). Many characters find themselves haunted by their history, and the lives of their ancestors.
Remember, and read the afterword for clarification, that this book was originally published in the 1960s. Abuse, domestic violence, and even rape were not treated by society (and the law) in the same manner they are now. Keep that in mind when you read the text.
Feel free to check out this eNotes summary here.