A Browserify developer uses the Browserify tool to compile node.js-style modules for use in the browser. They write modular and reusable code that can run both on the client-side and server-side, enabling a unified JavaScript development environment. They manage dependencies, bundle different JavaScript files into a single file, and use the require() function in the browser similar to Node.js. Their goal is to enhance the efficiency of web applications, improve load times, and ensure code maintainability. They also deal with source transformations, allowing developers to write code in an extended JavaScript syntax or other languages.