A hierarchy (in Greek: Ιεραρχία; this comes from ιερός-hieros, sacred, and άρχω-arkho, rule) is a way of ranking and organizing things or people. Beneath the top of the hierarchy, each part of it is below some other part. This turns out to be like a pyramid. It is a system to decide who can make decisions, and who is forced to comply with those decisions.
An example with people would be the structure of a company. There is the top manager, and there are a few levels of middle and lower management. At the bottom are the common workers. Another example would be an army that might have a general, followed by colonels, corporals, and sergeants, then privates.
In democracy this is done by educating people in the issues and then voting - in an election to choose leaders, or a referendum to actually choose one option from several. Competing power networks each form a political party and each offers only one leader or one option to the public, to simplify the issues to make decisions possible. After the decision, they typically do not fight it to the point of civil war, but wait for the next election.
In dictatorship this is done by asking one powerful person to make the decision and then agreeing to force everyone to follow it. Any who will not are exiled, imprisoned, or killed, even if the decision is not very important, since the refusal to follow is taken as a challenge to the power structure itself. There is only one power network and all others are forced to become part of it, or fight it. Civil war is much more common in a dictatorship than in a democracy.
In these examples, people who are higher up have more authority and power than people below them.