It is the search engines that finally bring your website to the notice of the prospective customers. When a topic is typed for search, nearly instantly, the search engine will sift through the millions of pages it has indexed about and present you with ones that match your topic. The searched matches are also ranked, so that the most relevant ones come first.
Remember that a prospective customer will probably only look at the first 2-3 listings in the search results. So it does matter where your website appears in the search engine ranking.
Further, they all use one of the top 6-7 search engines and these search engines attract more visitors to websites than anything else. So finally it all depends on which search engines the customers use and how they rank your site.