Website design is a very in-depth topic that goes far beyond the look of the site. It is also about the languages (html, php, javascript, css, and many more) used to construct the site and add functionality, and the structure of the code, files, and folders within the website. All these areas must work together seamlessly to produce a productive site that is easy to navigate, visually pleasing, search engine friendly, and upgradable.
So to answer the question of “What is website design?”, I would describe it as the planning and implementation of the steps necessary to create a synergy of look, structure, and functionality that meets the needs and expectations of the websites targeted audience.