"The Second Coming" alludes to the second coming of Christ. In the poem, this second coming of Jesus is seen as a chaotic event that rocks the world. In Things Fall Apart, the missionaries are bringing the church's message of Christ, and it's this very message that begins to tear the tribe apart. It not only pulls away members of the tribe, but it questions and contradicts the very foundations of the tribal belief system.
Historically, Yeats' poem deals with the devastation of World War I. Much of Africa had been colonized during the late 19th and early 20th century. However, with the cost and the effects of WWI, the European nations that had colonized the continent could do little to advance it. Things began to fall apart, which led to a troublesome post-colonial period.
An important theme in Achebe's novel Things Fall Apartis concerns the effects of the missionary influence and European influence on the traditional values and ways of the Ibo culture. "The center cannot hold" says the speaker in Yeats' poem, which is indeed the case in the novel, for not only does the structure of the village begin to collapse as a result of the incursion of the Europeans, but the protagonist doubts his very manhood, so much so that he despairs and commits suicide.