You can think of hierarchy as a kind of grandmother principle achieved thru the careful use of all the other principles. That said, it's actually very simply defined: visual hierarchy is the arrangement, contrast, and overall presentation of elements in a composition such that the relative visual importance of each element is clearly conveyed to the viewer.
By achieving good visual hierarchy, one simultaneously achieves good content flow, leading the eye from the most important elements to the least.

In the example below, the poster on the left is broken down on the right to demonstrate where my eye moves as I'm reading through. The thick blue line is the first read through, whereas the thinner light blue line is the secondary read through. Notice how my eye goes from the top to bottom, but I start from the largest object with the darkest values to the smallest objects with the lightest values. In this case, position on the page, size, and value are being used to force a visual hiearchy.

GDPE diagrams hierarchy content flow 20 20

 

In traditional prose text, laid out in, say, a book, visual hierarchy isn't necessarily needed as the eye generally knows where to begin, e.g. the first letter of the first word of the first line on the page. In the West, we generally read from left to right, top to bottom. No further content flow is needed:

spread.jpg

But what if the audience reads only Hebrew, Arabic, Japanese, or, I don't know...Ancient Egyptian hieroglyphs?

Or what if our audience doesn't read at all (think children's media)? In that case, we need to be creative and decisive in how we present and contrast elements. For an excellent example of how frustrating a lack of visual hierarchy can be, take a look at the below image from the Where’s Waldo series of visual puzzles:

Can you find Waldo?

Having some trouble? That’s because of one simple reason: lack of hierarchy. In this case, we know the conceptual focal point of this composition is Waldo, a goofy guy with glasses who likes to hide. But visually there is no focal point, there is no predominant color, form, or grouping of objects. And because there are so many figures in this composition, there is little to no content flow, so the eye is already struggling to distinguish different objects. You can therefore imagine that an excellent way to achieve hierarchy is to begin with a strong focal point, use a lot of white space to facilitate content flow, and to use contrast well to achieve an order of importance:

Leopoldo Metlicovitz, Calza- turificio di Varese poster, 1913.
Leopoldo Metlicovitz, Calza- turificio di Varese poster, 1913.