The best place to start in answering this question is to refer you to the poem from which the title of Achebe's work is taken. "The Second Coming," by William Butler Yeats, is a powerful dystopian vision of the kind of anarchy that Yeats saw breaking into the earth at his time of writing. Achebe quotes the following lines from this poem at the very beginning of his novel:
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 reference to the image of a falconer trying desperately to bring his falcon back under his command but failing as the falcon turns ever further away from him becomes an incredibly important symbol, both in the poem and the novel. Achebe uses it to refer to the way in which the influx of colonialism and the clash of cultures that occurs when Europeans arrive at Okonkwo's tribe brings with it chaos and anarchy as traditional systems of order are completely destroyed and chaos is left in the wake of this culture clash. You might like to consider, for example, the ways in which the church welcomes those that are excluded or made outcasts by the tribal religion. Again and again, the conflict between the tribal tradition and Christianity produces chaos and anarchy where before there had only been a system that worked and preserved harmony and peace.