Hierarchy is most easily defined as "any system of persons or things ranked one above another." It was originally used as a word to describe literal rank in government or similar organizations. For example, the King was on top, and everyone else was on the bottom, but in varying degrees of status. In design, hierarchy is very important to understand and use because we, as people, rely upon it to inform ourselves.
In our modern world, there is a ton of information coming at us all at once. Everybody wants to tell us their story or give us a message, and our overwhelmed human minds have adapted to filter out useless crap and retain the stuff that is easy and seemingly more important. So in essence, humanity has its own information air filter that tosses all the "similar" stuff into one pile (marked "ignore") and places the other "bold" stuff in another pile (marked "read this").
As designers, it is our job to understand this tendancy of modern man and work to accomodate it. This is where information hierarchy comes into play. In all designs, there is an item that is most relevant and an item that is least relevant. There is also everything in-between. If all items on a page are created with equal hierarchy, than none of them are noticed. They all look the same, and there is nothing telling the viewer "hey, look here first." Things become a clutter of information, become confusing, and ultimately the viewer feels frustrated and loses attention.
This is why we need hierarchy. We need an item that says "look at me first" and other items that allow that hero item to stand out. They allow it to stand out by assuming the role of being less important; they take one for the team and stand back while the hero shines.
Even if you have 8 items and somebody tells you "there can't be hierarchy because they're all equally important," make one of them bigger anyway. Give one of them more attention. Use it as an introductory item, at the very least in order to start the story of your design. Just use hierarchy. Study it. Master it. Use it to its fullest potential. It's not a difficult concept, but so many people don't understand it or forget to make use of it. If you ignore hierarchy, your design work will fall into that pile of sameness that is marked "ignore."
- Ryan Ford