Originally, Web pages were written in HTML, the HyperText Markup Language, which was conceived to describe text. And it's very good with text - in paragraphs, tables, and forms, and linking to more text. It can even embed images inside that text, but by itself HTML produces rather bland pages. (It can do some very basic manipulation of colors, for text and backgrounds, but that ability has been superseded by HTML's buddy, CSS[1].)
XML, the eXtensible Markup Language, is a very general-purpose language based on the same syntax as HTML, but it was conceived with different things in mind. As markup languages, they both describe information, but XML is best known for allowing everyone to use their own vocabulary to describe their information. It also has stricter rules than HTML, making it easier for programs to understand. A vocabulary expressed in XML is a dialect of XML.
XHTML is HTML as an XML dialect. It allows dialects to also be derived from itself, hence "eXtensible HyperText Markup Language." I'm showing you the latest version (5) of XHTML. It does have an HTML counterpart, with looser rules, but I see little point in that. (It would be important if your SEO client had an existing HTML page, though.) You can read about the differences if you like.
- See here for details on CSS.