There is a lot going on in the book "Things Fall Apart," and one of the main conflicts in the story is between the Igbo people's religion and the missionaries' Christianity. The Igbo people believe in many different gods which are mainly representations of some aspect of nature. Earth goddess, sun god, tree god, etc. That view is quite distinct from a Judeo-Christian perspective in which there is one all powerful God.
During Okonkwo's exile, he learns that white missionaries are going to be coming to his homeland. Their goal is the conversion of the Igbo people, and they have successes. In order for Achebe to show his reader some legitimacy to their success over the Igbo religion, he includes Biblical references, so that the reader can better understand how the missionaries are able to convert so many so quickly. It also grounds the story in realism. Christianity is a real world religion, so things that Achebe claims are in the Bible, had better be in the Bible.
Another reason is so that Achebe can draw some parallels between Okonkwo's life and Biblical stories. For example, God told Abraham to kill his only child (then God stopped him from doing it), and the elders had Okonkwo kill his adopted son. Lastly, Achebe can put Christian beliefs in his book, because he knows a lot about Christianity. It was a major part of his upbringing, family, and life.