the man at the head of a household: the owner of the house and all that belongs to it, with authority over the people in it and answerable to no one inside it
This is a compound word. It joins the Greek noun for a house or household (οἶκος) to the word for a master who holds full authority over those who serve him (δεσπότης). Together they name one particular man: the one at the top of a household. An ancient household was much larger than a modern family. It took in a wife and children, slaves and hired workers, storerooms and supplies, and often fields or a vineyard, and this was the man who owned all of it.
That is why one word covers scenes that look quite different in English. In some he is plainly the man of the house: he bars the door at night, keeps watch against a burglar, decides who eats at his table, and reaches into his own store of goods. In others his household reaches out into the countryside, and he is hiring day laborers, leasing a vineyard to tenants, or facing a complaint about wages. Greek needed no second word for the second set of scenes, because owning an estate simply was heading a large house.
Nearly every use sits inside a parable, and in most of them the figure stands for God or for Jesus himself. The word is not a religious title, though. It is the ordinary word for the man in charge, and the stories work because everyone listening knew such a man. Once, in Matthew 10:25, Jesus uses it of himself, contrasting his own standing with that of the members of his household, meaning his followers.
The man who actually ran a large house day by day, keeping the accounts and directing the staff, was someone else: the household manager (οἰκονόμος). This word always names the owner, never the employee.