API Gateway is the AWS service that allows interfacing an application's back-end with its front-end. The figure below shows an example of such an application, consisting of a web/mobile-based front-end and a back-end residing in a REST API, implemented as a set of serverless Lambda functions, as well as a number of legacy services.
The figure above illustrates the so-called design pattern Legacy API Proxy, as described by Peter Sbarski, Yan Cui, and Ajay Nair in their excellent book Serverless Architectures on AWS (Manning, 2022). This pattern refers to a use case where Amazon API Gateway and Lambda are employed together, in order to create a new API layer over legacy APIs and services, such that to adapt and reuse them. In this design, the API Gateway exposes a REST interface invoking Lambda functions which, in turn, modify the requests and the responses or transform data to legacy-specific formats. This way, legacy services may be consumed by modern clients that don't support older protocols.