Embedding Moesif dashboards into a React application allows teams to share insights conveniently within a developer portal by using iframes, ensuring that data visibility remains controlled through backend URL retrieval post-authorization. This process involves setting up a Node.js project with Express as the backend to fetch and provide dashboard URLs, which are filtered by company to prevent unauthorized access. The React frontend requires a Dashboard component that utilizes React hooks to dynamically retrieve and display the appropriate dashboard URL from the backend, based on a workspace ID prop. This setup facilitates the integration of multiple dashboards, allowing for easy switching and configuration, while Moesif's sharing features and workspace IDs streamline the embedding process.