Well to put it simply, aristocracy is a type of government in which the state is run by a small group of people who are supposedly the representatives of the masses.

The aristocrats where often prominent men and women in the society who were supposedly fit to to rule, primarily because of their position in the society. Aristocracy differs from monarchy in the sense that it's a group of people that are leading, and not just one, so the power is a bit decentralised.

It originated in Greece and it was a clear attestation to their dislike for monarchical rule. At a point democracy itself failed in Greece but aristocracy survived. Aristocracy is basically a government in which the ruling class lead the state, it's as simple as that.