Irony refers to what is said is in contrary to its meaning. Similarly, in the dramatic irony, there are differences in perspective. Actions of the character are understood by the audience whereas, the character does not.
In the Chinua Achebe's "Things Fall Apart", everything in the village of Okonkwo changes after Okonkwo's exile. More men are converted into Christianity from Umofia as white men enter the village. As Okonkwo exiles, he loses his grip to hold the village together and preventing the entrance of intruders.
Dramatic irony occurs when the things start falling apart after his exile and that his fall is identified prior. As a leader now Okonkwo lost his authority in his village by asking the village leaders to go to war.
Now that Oknokwo was on his exile he was able to relate with Ikemefuna on the feels of leaving own homeland. Just like Ikemefuna he becomes an exile and that in his absence much will change was not expected.
As Okonkwo doesn't take responsibility for his own actions he blames on his chi for everything.
"When Okonkwo is in exile, he ponders the tribe's view of his chi. He thinks that maybe they have been wrong- that his chi was not made for great things. Okonkwo blames his exile on his chi. He refuses to accept that his actions have led him to this point. He sees no connections among his breaking the week of peace, his killing Ikemefuna, and his shooting Ezedu's son. In Okonkwo's eyes, his troubles result from ill fate and chance."
In opposition to a strong leader, Okonkwo displayed himself as not as strong as he appeared to be. As a strong man, he leaves his village and when he returns he is opposite. Finally, as his village was falling apart he hung himself and dies like his father, without any honors.