Things Fall Apart by Chinua Achebe is what is sometimes known as a "postcolonial" novel, meaning that it addresses the effects of European colonialism and its aftermath on a non-western society. Set in Nigeria, Achebe's novel tells the story of how the Igbo people respond to the colonial situation.
The first main conflict within the novel is that of Okonkwo, who struggles to become a great man and warrior, despite his mediocre "chi" or spirit, in a way that defines success in a traditional Igbo manner, but also puts him in conflict with tribal custom.
Next, we have a conflict between traditional Igbo religion and the newly introduced religion of Christianity.
Another type of conflict is based on gender, with the Oracle of the Hills and Caves being an example of female power and Okonkwo of a male who suppresses his feminine side and thus is considered unbalanced by Igbo standards.
Finally, we have a conflict between the white colonial powers and the Nigerians.