SEO (Search Engine Optimization) is just that, optimizing your website for search engines. The search engines crawl the web and fill their database with the information from the various sites on the web. Search Engine Optimization does not cost anything although you may hire someone to perform these tasks for you. SEO is sometimes referred to as Organic since these is the information that you are not paying the search engines to list for you. Your ranking in organic SEO is based on many factors including how many other sites are going after your keywords.
MOZ Link Explorer: https://moz.com/link-explorer
Website Grader: https://website.grader.com
SEO Web Page Analyzer: http://www.seowebpageanalyzer.com
Power Mapper SEO Checker: https://www.powermapper.com/products/sortsite/checks/seo-checks/