When searching for a business online, most people aren't typing the actual name of your business into the search engine....chances are, they don't know it. So your focus in optimizing your website for keywords shouldn't just be the name of your site. (On the other hand, if you do search for your business name online, and it doesn't come up first in the results, take action quickly!). Most people use at least two words, and sometimes a whole phrase or sentence. Many SEO/Internet Marketing companies help businesses establish presence with just one word, like "insurance"...but this can be very competitive and expensive to do.
Long tailwords are basically key phrases related to the core keyword, that people may use to describe what they're looking for to the Search Engine. For example, to find insurance services in South Riding, VA (Loudoun County), one might just type in "insurance". But that doesn't really give any localized or useful results. Using "loudoun insurance" or "south riding insurance" gives far better results, and something like "loudoun allstate home insurance" will deliver the best results. These multi-word phrases should be targeted for your business, along with the single keywords, and usually deliver pretty good results.
This particular example highlights a Loudoun Insurance client of ours, NOVA Insurance of South Riding, VA, who's search results went from zero to essentially "owning the market" with all relevant key phrases and long tailwords for this area, within 1 month (i.e. all relevant searches appear high on the first page of all search engines).