The significance in relation to Yeat's poem is the implication that nothing lasts forever.
Turning and turning in the widening gyre
The falcon cannot hear the falconer;
Things fall apart; the centre cannot hold;
Mere anarchy is loosed upon the world,
The blood-dimmed tide is loosed, and everywhere
The ceremony of innocence is drowned;
The best lack all conviction, while the worst
Are full of passionate intensity.
Yeats wrote Second Coming in the aftermath of WWI, and the theme of the poem is very similar to the theme of the novel in Things Fall Apart. There was a reason the author used the line in his title, and there are definite parallels in the two pieces of literature.
Yeat's poem is based on changes made by war, and it charges that when anarchy comes into play, the function and focus of a community shuts down. Thus, things fall apart. Society fell apart because the people shut down. They allowed the government to control their actions.
In the novel, the breakdown of African society occurred because the community didn't stand together. They didn't stand up for their beliefs in their religion or their government. The missionaries were allowed to change their ways............ the poem states, "things fall apart when the center cannot hold." The center, or the focus of the community split, it divided. Obierka describes this on page 176, claiming that the white man had had put a knife to the things that held them together, and as a result they had fallen apart.