A web page's structure is dependent on HTML. You knew that already. But unless the structure is constructed carefully and according to standards, it could fall apart. Making sure that your site is correctly rendered in whatever browser and on whatever operating system your audience chooses means making this bullet-proof. Making a site bullet-proof means...well...making sure your site renders correctly in whatever browser blah blah blah.
Making a site bullet-proof is harder than it sounds, but easier than people make it out to be.
Start by using the HTML tags for their intended purposes. Paragraph tags for paragraphs, tables for tabular data, lists for lists, and so one.
Then use classes and IDs that describe the content, not its position on the page.
Use header tags in the order that they appear, not by the size you want them to have.
Then close all your open tags, use title and labels liberally, use tag elements to further clarify meaning and intent, and make sure everything works in every browser.
That's what I do!