Headings indicate priority and structure on a page. Heading 1, or "H1", is the most important. There will only be one H1 on a page, and it should convey the clearest representation of what the page holds.
The latter headings (H2-H6) are used like an outline–see example below. Visual representation should match with the numbered priorities: H1 should look more important than an H3, for example. (If this isn't the case, contact a developer or designer to adjust your CSS templates.)
Imagine all of the content except your headings was stripped away (incidentally, this is one common way alternative devices navigate web content). With other content gone, your headings should convey an accurate outline of your content. For example...
Look at the (admittedly bloated) title below. How would you make this simpler? Try going through each part and asking if it's truly essential.
The University of Virginia Library's Libra Open Access Content Repository Faculty Course Instruction Grants
For example, we probably know it's UVA by context (header, logo, etc.) so:
The University of Virginia Library'sLibra Open Access Content Repository Faculty Course Instruction Grants
Does the name of the tool really matter in this context? (It depends...)
LibraOpen Access Content Repository Faculty Course Instruction Grants
What about instruction–are all three words, "Faculty Course Instruction" essential at this point? What can we cut without losing the essential message?
Open Access Content Repository
Faculty CourseInstruction Grants
Finally, "Content Repository" is more about the end than the means. Does that matter at this point in the process? Perhaps not.
Open Access
Content RepositoryInstruction Grants
Better?
Open Access Instruction Grants