A standards based web design process is one which aims to present your website in the most effective and efficient way possible: Properly displaying your content across multiple devices, platforms, and browsers- Including users with disabilities. The code aims to overcome all these technological disparities to present the site consistently.
These standards are administered by the World Wide Web Consortium, or W3C, an international organization founded by the guy who basically invented the World Wide Web in 1989, Tim Berners-Lee.