A Noble family is a family who are related to the Royal family, but they are ranks below King. Nobles usually are less known then Royals but in some cases nobles were more well known. Some "Noble families" are not noble. Take the Medici family and the Borgias.Thoes to family's are known as Banking families and aristocrats. Those families are Rich but not a member of Nobility that is recognized by the King/Emperor.
Nobles were always recognized as lower families of the King/Queen. Nobles usually ruled Duchy's, Counties, and principalities. Nobles were usually given a "House" which was of course a noble house. Nobles usually worked as advisors to the King, and land owners. But some families did not work at all because they were really rich. But not all nobles were rich. Some Nobles were very poor. One of the richest claim to be noble families were the Medicis. The Medici's ruled Tuscany, Milan ect. The Medici's were pretty much common people, but they were richer than most monarchs at there time until there fall in the 1700's. One of the poorest family's were a period of time was the Bonaparte family. They were poor until Napoleon became Emperor of the French.
Noble families had plenty of power depending on what land they ruled. The rich Duchy of Burgundy was a major power spot because of how big to Duchy was. Another power spot was the Duchy of Milan and the Duchy of Luxembourg. But some Nobles had little to no power. Mostly because most nobles are given an style like "Lady" that is non hereditary.