The Nobles are Britannia's highest position. They enjoy absolute power over everyone that is not a noble, even a native Britannian, and can only be surpassed by other nobles of higher position. Also, all nobles are extremely wealthy and have wealth far above most Honorary Britannians and native Britannians. This economic position is not necessarily hereditary of the noble's previous family (as evidenced that some nobles are born nobles or their position is not hereditary) although the method by which this wealth is attained isn't specified (it could be that all nobles have high paying posts or that all nobles receive economic tribute from Britannia or maybe a combination of both). Politically the nobles are the ones who govern all of the Britannian Empire, though militarily and secretly it is the Emperor and the Geass Cult who have control.
After Lelouch became the emperor of Britannia, the Britannian aristocracy was abolished. Notably many nobles, excluding the ones Geassed by Lelouch, made an attempt to overthrow Lelouch, only to be quickly vanquished.