The concept of incremental architecture in building websites emphasizes the importance of making key architectural decisions during the project, rather than waiting until the end. This approach allows teams to work on different systems in parallel, simplifying complex workflows and enabling faster delivery of business results. By evaluating systems incrementally, developers can synchronize different work on different systems, creating a modular architecture that fosters greater flexibility and efficiency. The example of Jaxxon, a market leader in men's jewelry, demonstrates the success of incremental architecture in building a fast, secure, and scalable website with Gatsby and Contentful.