The formation of an Oligarchy is the beginning of feudalism, when a particular group of people native to this part of the country take the power and hold it by any means necessary. This benefits greatly local defense, since this group undertakes the obligation to pay any units from the central army stationed there, and is interested in helping it out by any means necessary. After all, they defend their interests!
Adopting Oligarchy is necessary to progress further down the tree, so it is generally a no-brainer. To make best use of it, keep a unit stationed in each city - this will offset its maintenance cost, freeing up Gold for other, more important purposes. And, of course, it greatly increases the defensive power of a city, which is extremely useful for defense-oriented empires in all stages of the game.
Oligarchy is a form of government in which a small segment of society has all of the power. Power might be held by a specific family or tribe, or people of a certain religion or from a special caste. Some city-states in ancient Greece were oligarchies, where all power was in the hands of a few elite families. Apartheid South Africa would be a modern oligarchy, the white minority holding all of the power. Pre-9-11 Iraq too was an oligarchy, with power concentrated in the hands of members of Saddam Hussein's family and tribe.