Part of the issue here is that the way you use headings differs in HTML4 and HTML5. As you’re probably working with HTML4 right now, let’s deal with that first.
In HTML4, headings are used to create a structure in a page. Because of that, if you want a meaningful structure, you need to use headings in a proper, hierarchical manner. Try to think of this as an analogy. Consider the page as a book. The title of the book would be an H1. The next ‘subsection’ of the book would be the chapters. Each chapter would be an H2. Individual chapters might be broken down into sections. These would then be H3s. And so on.
If you tried to make a book in which you labeled the book as ‘Chapter 1’, and then had the book title as a subsection of that, it would be absurd. Likewise, if some of the main divisions of the book were chapters, but one was the book title and others were subsections, your table of contents would be very strange.
In our analogy:
H1 = book title
H2 = chapter title
H3 = section of chapter
h4 = subsection of these sections
and so on.
You can’t have a subsection without a section first. You can’t have a chapter title with the book title first.
There is a bit of disagreement about what the H1 should be used for on a web page. Most developers think that the H1 should be the main title for the page. A minority of developers think that the H1 should be the title of the website. I think it can depend on the type of site. If, for example, you were building a three page website for ‘DoubleDee - Aviator’, that might be the most important thing about each page, and you could use the H1 for the site title. A website for a University, however, would probably use the h1 for each individual web page, because the title of the page is of more importance than the name of the university. However, this whole thing is up for debate.
If, however, you use the H1 for the site title, you should not have any further H1s on a page. If you use H1 for the page title, you could conceivably have more than one H1 (although it’s bad practice, IMO) if your page consisted over several unrelated sections of equal importance (although why they would be on the same page, I’m not sure).
In HTML5, however, things have changed. The structure of the page is no longer created from the headings. Thus it’s perfectly normal to have multiple H1s on a page. But HTML5 is too large a topic for me to go into here.