The purpose of a web API in application development is to enable seamless communication between different software components, allowing for data exchange and functionality integration over the Internet. Web APIs provide developers with standardized protocols to access services and resources from various platforms, facilitating interoperability and enhancing overall application capabilities. They empower applications to interact with external systems, including databases, third-party services, and cloud solutions, leading to richer user experiences and simplifying development processes by leveraging existing technologies for creating innovative solutions.