Regarding "Macbeth," explain the power or authority of the position Thane of Cawdor. In today's terms is it like a Governor of a state or other...

According to the official web site of Cawdor Castle in Scotland, the duty of the thane was:

the equivalent, in Scotland, of a feudal baron holding lands from the Crown. A thane was frequently the chieftain of a clan, always the administrator of his district, usually an influential individual with power of life and death, and was only answerable to the King or to his deputy or to God.

The thane was overseer to lands and property granted to him by the king. He would not be a mayor or a governor but something sort of in between. Scotland has five ranks of peerage, all subject to the monarch:

1. At the top is the Duke, who is usually a relative of the monarch. He could be considered the same as a state governor in the US.
2. Then the Marquess, who oversees a border territory (or "march"). I don't believe we have anything to compare. Under the Marquess is the
3. Earl (or Count), who administers a shire or province. A shire is the equivalent of a county in the US. He might be compared to a US Member of Congress.
4. Then comes the Viscount, who is the deputy of the Earl. If we had county mayors, that's what this person might be like.
5. Finally comes the Thane (Baron in England). He is overseer of a parcel of land given to him directly by the king. He is more or less a wealthy landowner. If you're familiar with old TV Westerns, think of him as being like Ben Cartwright on "Bonanza."

Towns would also have mayors, aldermen and other officials. Church officials would have power too.