An API gateway is one part of an API management system. The API gateway intercepts all incoming requests and sends them through the API management system, which handles a variety of necessary functions.
Exactly what the API gateway does will vary from one implementation to another. Some common functions include authentication, routing, rate limiting, billing, monitoring, analytics, policies, alerts, and security.
In organizations that follow a DevOps approach, developers use microservices to build and deploy apps in a fast-paced, iterative way. APIs are one of the most common ways that microservices communicate.
Additionally, modern cloud development, including the serverless model, depends on APIs for provisioning infrastructure. You can deploy serverless functions and manage them using an API gateway.
In general, as integration and interconnectivity become more important, so do APIs. And as API complexity increases and usage grows, so does the value of an API gateway.