There are several forms of conflict in the novel The Color Purple. Chief among the types of conflict are man versus self. However, all of the other forms of conflict can be found in different aspects of the book.
As noted above, the primary conflict is man versus self, as Celie tries to understand who she is and what value her life carries. She argues with her self worth because she is ugly, and black, and can't do much more than a house wife can. She was raped by her father at a young age, so she also struggles with those demons, and the loss of her children. As she grows up, the only real love she knew, before Sug Avery, was the love she felt for her sister. When her sister Nettie is taken away, a glimmer of man versus man is shown. Mister wanted Nettie to sleep with him, she fights back, and Celie loses touch with her sister.
As the story progresses, you notice Sug Avery's singing secular music, that, at the time, was very taboo and risky. She also has a romantic exchange with Celie, also taboo. This portion of the story showcases man versus society. Essentially, both women are going against the status quo by being braisen, singing "filthy" songs, and being intimate with each other. Sug Avery is rejected by her dad, a pastor, because of her life choices. That element of rejection is also an example of man versus man.
Man versus nature is seen when Celie finally breaks free from Mister's grasp, and tells him that until he does right by her, all that he touches will fail. At that time, his crops begin to wither, his animals die, and his land becomes barren. The last example of man versus nature is within the Olinka village where Celie's children live. When the village begins the industrialized phase, Celie's children's adoptive mother becomes ill from the chemicals and pollution after industrialization.
The central conflict of the novel is Celie's internal conflict. One way to support this idea as the central conflict is to point to the fact that the novel's resolution hinges on the resolution of this conflict in particular.
Celie's development into a person capable of self-love and forgiveness is, effectively, the resolution of the novel's central conflict. This growth in her character is tested when Shug has an affair with a young man, but it is at this moment when Celie's growth is most clearly defined and proved.
Other conflicts are external. There is a "man vs. man" conflict that begins the novel as Celie is abused at home and again in her marriage to Mr. _____.
Another external conflict, which symbolically parallels Celie's internal conflict, relates to Celie's biological family. They return in the end, closing a circle of loss, estrangement and disenfranchisement.