Vodstock is teaching the very basics of html here, and your instructor is talking about XHTML- an updated and expanded version of html. You can read about the differences between html 4 and XHTML, and why you need that statement at the beginning of an XHTML document, here:
http://www.w3.org/TR/xhtml1/
If you're just going to use pretty basic htrml and some tricks here and there, you don't need to worry about DOCTYPE declarations.
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