The answer above is a great one, and the example of Saudi Arabia presents a wonderful example as well of despotism. Many of the regimes in the Middle East are in fact good examples of it, where the power is concentrated in the hands of an elite whether they are a theocracy or, as in the case of Saudi Arabia, a monarchy.
But the King of Saudi Arabia acts mainly in the interests of his own family and the closest pieces of the royal family, enacts rather brutal policies against his political enemies, keeps the people under a very tight lid with almost zero civil rights, and no one has access to the reigns of power outside of the royal family.
The term "despotism" refers to any sort of a government that is absolutist (see link) or totalitarian in nature. These are types of government in which power is kept very centralized, typically in the hands of one person.
In addition to having this relatively technical meaning, the term "despotism" also has very negative connotations. We would rarely refer to the Kingdom of Saudi Arabia, for example, as a despotism. This is because we (in modern times) tend to use the word to refer to a system where A) power is concentrated in the hands of one person or a very few people and B) where that power is very clearly abused so as to help those in power rather than their people.