The title of Achebe's novel Things Fall Apart is taken from William Butler Yeats' poem "Second Coming." According to Enotes:
The title of the novel echoes W. B. Yeats’s poem “The Second Coming,” which describes history as a succession of gyres, or spirals. Achebe applies the image to Africa as the nineteenth century traditional world of the Igbo people gives way to the colonial forces of the twentieth century.
The first stanza of the poem reads:
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.
The analogy of the falcon and the falconer is related to the Igbo people and their culture. Just as the spiraling gyre spins the falcon out of control, the violent male tradition and impending Christian colonialism cause the Igbo people to become disoriented from their core values. Over time, they forsake their traditional communal culture, becoming increasingly more dependent on outsiders.
As you read the novel, look for things breaking, being torn or divided: kola nuts, water pot, Ikemefuna, etc...
"Things Fall Apart" is a quote from WB Yeats' poem "The Second Coming". The line reads
Things fall apart; the center cannot hold
which means that nothing is stable in life. Everything is in a perpetual state of change; there is nothing firm or stable to rely upon.