In UX and UI design, Hierarchy prioritizes content (which comes first!) and UI design and visual elements like buttons, navigation, etc.

An easy way to demonstrate hierarchy is in the form of a Site Map. Also traditionally used as XML files to improve a website's SEO, site maps today are an integral part of UX design.

For our purposes, a Site Map is a visual representation of the structure and hierarchy of a website’s navigation. Simply put, Site Maps are simpler than Information Architecture (IA).

IA comes into play for more complex sites, as it deals more with both content and functionality. Taxonomy, grouping, storing, and labeling of content comes into play for IA. Sitemaps are simpler and outline the main pages and subpages of a website. 

Why does hierarchy in all of these forms matter? Without proper structuring, labeling, and visual prominence information would be a PAIN to get through! Can you imagine not being able to easily scan an e-commerce product page for a "Buy" button? Or to have to read through paragraphs of text to discern the time and location of a movie screening? Without design, information becomes much more difficult for us as users to sort through. 

Through the use of hierarchy in your design and hierarchy in your structure, important information and design components become simple and elegant.