Amazon API Gateway helps developers create and manage APIs to connect backend systems like EC2 and Lambda to mobile, web, and server applications. An API in API Gateway consists of resources and methods. Resources represent logical entities that can be accessed via HTTP verbs like GET and POST. Methods map API requests to integrations with backend systems. API Gateway handles request/response mapping and provides benefits like monitoring, security controls, and scalability without servers. Pricing is based on monthly API calls and data transfer. Caching can reduce costs for frequently requested data.