When you enter a search term into Google, Bing, or any of the other search engines, they perform a complex algorithm to determine which pages are most relevant to your search. As part of their calculation, the search engines consider the amount of times your search terms appear on web pages (in the main copy and in headings), in URLs, and in hyperlinks - the pages with the most keywords, score the best ratings. This is simplifying the process somewhat, but the fact remains that if you have a high density of carefully chosen keywords in your web pages, you have a better chance of being rated highly.
Search Engine Optimisation (or Search Engine Optimization if you use the American spelling, which seems to becoming the standard), is the careful construction of your web page code, links and copy so that your web pages score highly in searches. So SEO copywriting is the art of writing copy that is keyword rich.
One of the problems with SEO copywriting is that the need to repeat certain key phrases and terms can make sentence structure awkward and unwieldy for human eyes. Although you want your web pages to achieve high rankings, ultimately, it is a human being that will read them, not a search engine. Having a page 1 result is of little use if your copy is inaccessible and off-putting.
So when you are looking for an SEO copywriter, it is important that you choose a writer who can skilfully insert keywords without disrupting the flow of the copy. Good SEO copywriting should barely be noticeable - if the keywords are jumping out at you and making sentences 'clunky', the copy isn't working - it may appeal to Google, but it is already starting to grate with you. And so it will annoy your customers too.
Having worked as a freelance copywriter and SEO copywriter for several years, I have developed a knack of structuring sentences so that keywords are included with subtelty. Sure, sometimes it is difficult to avoid keywords sticking out like a sore thumb, but with a bit of perseverence and a little knowledge of how Google treats punctuation, it is usually possible to create SEO copy that appeals to humans and search engines alike.