For most organizations, a front page listing on Google is very valuable. Search engine optimization is the process of improving your site ranking in search engine queries: when potential customers enter the primary search terms related to your business, your site ranks (ideally) on the first page of Google's search results.
SEO is both an art and science, particularly because the Google search algorithms change over time, meaning continuing tweaking and management is necessary. Through a process of analysis, social media activity, link building, blogging and website changes, Flourysh works to increase your website's ranking on Google. Search terms are tracked on a daily basis and strategy updated accordingly.
Since Google aims to return the most relevant and useful search results for a particular query, SEO is, implemented properly, about the larger picture of 1) understanding your customer's needs (so that you know what search terms are useful), 2) ensuring that your site really does provide the most useful and relevant information related to those search terms, and 3) making sure that you have all of your technical bases covered. There are many SEO companies out there that promise overnight results with "no effort" on your part - seldom do those stories have happy endings.
SEO is a long-term and ongoing process. Depending on how competitive the search terms are, it may take anywhere from 6 to 18 months to start seeing results. During this period it is advisable to run Google Adwords for the search terms to ensure that customers find your business when searching on Google.
For more information, here is a case study showing an SEO project Flourysh undertook for a client.
Also, here are some useful links to excellent explanations on the topic: