AWS Gateway is a versatile tool for building scalable APIs for modern web and mobile applications, allowing developers to create RESTful APIs that expose data and business logic. It supports various HTTP methods like GET, POST, PUT, DELETE, and HEAD, and integrates seamlessly with other AWS services such as S3 and DynamoDB to enhance API functionality. The process of building an API involves creating an AWS account, navigating the AWS Management Console, and configuring the API with the desired HTTP methods and Lambda functions. The provided code example demonstrates handling GET and POST requests to manage user data, and deploying the API involves selecting a deployment stage and using the generated endpoint for testing. Additionally, the text highlights the potential for API monetization and analytics through a platform like Moesif, which offers deep API observability and insights, making it a valuable tool for growing an API business.