A steward is the chief servant of an estate: they are responsible for the condition of the buildings, the productivity of the land, whether the taxes are being paid, and at least in the early period, they were also in charge of the household and thus managed all the staff. 

However, the term can also be used to describe more illustrious offices: in the UK, the Lord Steward is one of the highest-ranking officials of the royal household and historically both carried out normal stewardly duties (for the king, mind you) and carried messages between King and Parliament and swore in new members of Parliament; the Lord High Steward is one of the Great Officers of State, outranking even the Lord Chancellor, responsible for bearing the crown during coronations, historically responsible for trials of peers in the Lords, and attached to the Earldom of Leicester since the 12th century. 

In Holland, Norway, Denmark, etc. the etymologically equivalent term – statholder – referred to an official appointed by a feudal lord (more often king) to govern part of their estate, essentially a royal governor. 

In the real world, the closest thing to maesters were university-educated priests, who were among the literate elite and thus invaluable in running both secular and church bureaucracies. There isn’t exactly a Hand of the King analogue, because historically no one gave out that many powers and authorities to just one man. The Hand is like the entire Privy Council rolled up into one.