Count is the lowest rank you can have in the game. All Dukes and Kings hold at least one province as a Count. Without a higher title (such as Duke or King), a Count cannot have vassals and is subject to either a Duke or (more rarely) a King. Every time you conquer a demesne you gain the title of Count of that place.

If you hold enough titles in the same geographic region you can try to create a Duchy, promoting you to Duke and changing your sovereign, since Dukes cannot have Dukes as vassals.