The model of cloud computing that offers a platform for developers to build and run applications is known as Platform as a Service (PaaS). PaaS provides a comprehensive development environment in the cloud, allowing developers to focus on coding, deploying, and managing applications without worrying about underlying infrastructure. This model typically includes tools for testing, collaboration, and application hosting. By simplifying the development process and ensuring scalability, PaaS accelerates time-to-market for software solutions, enabling businesses to innovate while minimizing resource allocation to infrastructure management.