Basically different browsers treat the same markup in slightly (or radically in some cases) different ways. What you are being advised here is to ensure that your browser is capable of creating a Document Object Model (DOM), which is similar to the DOM provided by a browser. If I were you, I'd look to check the ability to produce the DOM in a fashion that is compatible with a standards compliant browser, in other words don't test it against IE6 (I nearly said i.e. don't test... but that would have been too ironic).
What you could do is render the DOM you produce out, and then compare it to the DOM dumped out when you render it in the browser of your choice. To do this, you can dump out the document using this
] script from the browser.