In most cases, a website is a marketing tool. A website design should be about converting visitors into new clients and customers or getting you a lead or contact information.
The other main thing that needs to be done is getting people to visit your website in the first place. There are a number of sources of traffic - Facebook, LinkedIn, directories, Adwords - and one of them is from being found in the main search engine result pages ( SERPS ).
SERPS get you good quality visitors, because these are people who are pro-actively searching for what you're offering. And the main results, rather than the paid ones, are generally better trusted.
Search engine optimisation ( SEO ) isn't always the best solution for a business, as it can take a lot of effort to get good exposure which isn't always viable. But it should always be looked into because of the quality traffic it provides.
Increasing attention and website visitors from SERPS is a combination of things done externally ( links back to the website and mentions in social media and directories ) and the way the website itself is built, which comes back to the design.
These are the best steps to follow ...