Frankly stated, SEO, or Search Engine Optimization is the process of getting your companies website found when people search for certain terms on Google (or any other search engine like Bing or Yahoo).
As an example, if you are a third party logistics company that specializes in frozen food service distribution, then you want your name to appear in Google's Search Engine Results Page (SERP) when customers are looking for the type of services your company offers. SEO is the process of creating and positioning your site to rank well on Google's search pages - organically. If someone goes to Google and searches on "frozen food logistics" you want to be the first company that potential customer sees on the page.
You will notice there are other listings at the very top and right margin of the Google results pages. Those are ads that company's pay for to be located in those areas. Each time someone clicks on one of those links it is costing the company $.50 to several dollars for the privilege of a user clicking on their link. Organic search like we are talking about here is the process of getting your site to rank high on the page without paying any of Google's pay per click fees.
So what is Google looking for to rank your company highly as a logistics software company, or as an ecommerce order fulfillment provider? There are two main things: relevant content on the site related to the search terms and site credibility, which means there are other sites with "backlinks" to your site. Backlinks are a type of "social proof" that other website are linking to your website because it is credible and worthy.
So what to do? Figure out what "keywords" your customers are typing into Google that relate to what services you are selling and add related content to your site in the form of blog posts or new pages that will show Google you have authority on those topics. Then, work to get backlinks to your website from other credible websites. This can be done by responding to blog and forum posts and getting your website address out there. Both these strategies are complimented by a well executed social media strategy.
These two ideas are just barely scratching the surface of ways to improve SEO for your site. The benefits of ranking well with Google are almost priceless, yet easy to achieve when executed properly.