The role of script languages in web programming is to provide a means to create dynamic and interactive content. Languages like JavaScript, PHP, and Python allow developers to implement features such as animation, form validation, and data manipulation without needing to reload the webpage. This enhances user experience and delivers real-time information. Additionally, script languages facilitate communication with databases and server-side processes, enabling the development of complex web applications. Their versatility and ease of use make them essential tools for modern web development.