Feudalism is a system of government and of organizing society that dominated Europe in the Middle Ages. It was also important in other areas of the world, notably in Japan. Feudalism was a system that was based on personal relationships between superiors and inferiors. It was a system that was much more complicated in reality than it was in theory.
In theory, feudalism created a system of obligation and obedience from the lowest person in society all the way up to the king or queen. The way it worked was that monarchs knew that they could not control all of the land in their kingdoms. Therefore, they gave some of that land to a group of powerful aristocrats. The aristocrats came to be called vassals of the kings and the kings were known as the lords of the vassals. The king would promise to protect his vassals and their lands and to treat them with justice. The vassals would promise to obey the king and be loyal to him. They would also promise to give him military assistance when needed.
These aristocrats who were vassals of the king would then typically give part of their land to vassals of their own. They would be lords to their own vassals and the two would swear the same sorts of oaths that kings swore with their vassals.
In theory, this meant that each person was bound to obey the person above them in the feudal hierarchy. Things did not always work this way, however, since vassals were always trying to get more power relative to their lords and would be disobedient when they thought they could get away with it.