The Checkly web app's performance was significantly improved after a half-day of optimization efforts, resulting in a Lighthouse score of 100 from an initial score of 34. The optimizations focused on reducing bundle size by selectively importing modules and libraries, and implementing code splitting to reduce the amount of JavaScript loaded at each route change. These changes were made possible with tools like Bundle Analyzer and Webpack's BundleAnalyzerPlugin, which helped identify areas for improvement. By targeting specific areas, optimizing, measuring results, and iterating, the team was able to achieve a substantial performance boost, resulting in faster times to first paint and better overall user experience.