SEO (or Search Engine Optimization) is the process of tuning website pages to have a better chance of showing up as top results in searches for targeted keywords. There's off-site SEO and on-site SEO, which is more technical. Much of SEO has to do with website content and optimizing a website to be an authority in a certain niche/industry.
Your website's design can affect SEO because it needs to load fast but the goal of all SEO is the be the clear result that search engines will want to make the top result. Content should be clearly visible and the page should serve the needs of the website visitor.
When you optimize a website, you're looking at a number of factors:
Included with SEO should be conversion optimization. If you can add calls to action or make changes to a page to increase the number of conversions with existing traffic, then adding SEO will be much more effective because more of that new traffic will convert to leads and sales.