Today, when we speak of an oligarchy, we tend to think of a corrupt government that is run by a very few wealthy individuals. The term is most often used today when referring to the situation in Russia where Vladimir Putin and a few very rich "oligarchs" seem to have all of the power.
In Ancient Greece, an oligarchy was not like this. It was more like a democracy in which the right to participate in politics was limited to those who had a certain amount of money. The ancient Greek poleis that were run by oligarchies were not run by a small cabal of powerful people. Instead, they were fairly democratic in that they were run by elected officials. However, only people with a fair amount of money were able to run for office or to vote.
So, our current vision of oligarchy is of a government in which power is taken corruptly and held by a very few people. A Greek oligarchy was more of a democratic system from which the poor were excluded. It was not as democratic as we are today, but it was much more democratic than we would think given our current understanding of the word "oligarchy."