Which AWS service provides domain registration, DNS routing, and service health checks?

The AWS service that provides domain registration, DNS routing, and service health checks is Amazon Route 53.

Here are the steps to explain how it works:

1. Domain Registration: Amazon Route 53 lets you register domain names such as .com, .net, .org, etc. When you register a domain, Amazon Route 53 automatically creates a hosted zone that has the same name as the domain.

2. DNS Routing: After registering your domain, you can use Amazon Route 53 to route internet traffic for your domain to your resources, such as Amazon EC2 instances, an Amazon S3 bucket, or another website. You do this by creating "record sets" that point your domain to these resources.

3. Service Health Checks: Amazon Route 53 can also monitor the health of your resources and only route traffic to resources that are healthy. If a resource becomes unavailable, Amazon Route 53 can route traffic away from the unhealthy resource and to a healthy one, improving the reliability of your application.

In summary, Amazon Route 53 is a scalable and highly available Domain Name System (DNS) web service that connects user requests to infrastructure running in AWS.