"That was many years ago, twenty years or more, and during this time Okonkwo's fame had grown like a bush-fire in the harmattan"
GNU Free Documentation LicenseBrush-fire - Credit: Ikiwaner
The harmattan is a hot and dry trade wind that blows from the northeast through the western Sahara desert of Africa.  The harmattan is the strongest in late November to mid-March.  The wind carries with it a very fine dust that gets in every nook and cranny when it passes through villages.  The dust in the wind can limit visibility and even block the sun. 
This reference to the harmattan is used in a cultural simile.  During the season of the harmattan, a fire would travel and grow very fast because of the fast winds.  The wind carries the bush-fire and would make the fire almost unstoppable.  This fast growing fire is compared to the speed with which the fame of Okonkwo grows after he “threw the cat.”