Search engines like Google, Yahoo & MSN have self created index’s with your business or company website listed in them. The search engine crawler organises each website with relevant keywords relating to your website and ranks the keywords by relevance.
So when a user types the relevant keywords into the search engine it generates results relating to the keywords. If your site is indexed with this searched keyword your site will rank in the search engine results page. If multiple sites rank for these keywords the search engine takes how trustworthy your page is into account.
The Process of ranking is more complex than that, No seo company knows the exact formula the search engines use to rank the websites, so guaranteed ranking number 1 should never be trusted as it cannot be successfully done for multiple websites as the formula for ranking is constantly changing as well as your rankings.