THE IMPORTANCE OF HEADERS
Headers, like a number of aspects of web design and SEO, have a dual purpose: They let bots know the importance of content, and they provide interest to human users. Having your content structured with headers provides some eye candy to users and clarity to search engines.
THE MAIN HEADER: H1
H1 is the first and main header of your web page that you should use. It tells users briefly what the page is all about, and it lets bots know what the main keyword of the page is. What keyword you put in the main title depends on what you're attempting to achieve by having that keyword. If it's for ranking organically, then you should do plenty of keyword research to find out which keywords have traffic: High to low, depending on your ranking strategy. If it's informational or a bog post for your online community, then you can cater completely to the user. Wise Tip: For every article you write for a search engine, you should write two more for a human, but never make the articles you write for bots too boring for humans.
SUPPORTING HEADERS: H2-H6
H2-H6 So far, I have the sequence of H1-H2-H3-H3. This is completely on purpose. H1 is the main subject, H2 is the supporting subject, and H3 is below the H2 subjects, and I can go on and on in descending order, or it bring a new supporting subject (H2) under the the main subject (H1). Most users don't read everything on the page, and just skim through to the interesting parts they like, so there's a great advantage to having headers structured in such way that makes it easier for users to find the content they want on the page.
CONCLUSION ON HEADERS
You don't have to get extremely technical, and you can definitely break the order of things, or disobey the H1 rule. The key is to let the content dictate what's needed. There are many great articles that don't make use of sub-headers (H1-H2), and that's okay if you're providing real value to the user.