Since heading tags typically make text contained in them larger than normal text on the page, this is a visual cue to users that this text is important and could help them understand something about the type of content underneath the heading text. Multiple heading sizes used in order create a hierarchical structure for your content, making it easier for users to navigate through your document.
Nice work Laura! This is going to be a great series. I'm working my way through SEOmoz's Advanced SEO Training Series (videos) Vol. 1 & 2 to build upon the advice and guidance that you and your team provided to me during my time at Yahoo!. Now many others will benefit from your knowledge, experience and passion for SEO strategy and tactics. Best wishes for great success in your new role.