Amazon Route 53 is a cloud service that provides DNS and traffic routing for applications. It allows users to define multiple routing policies and configure health checks to ensure high availability of services. Datadog, an integration tool, fully supports Route 53 by pulling in CloudWatch metrics and providing full support for DNS logs. Users can monitor Route 53 health and performance metrics, analyze DNS activity with Route 53 logs, visualize key Route 53 log data, and monitor resolver logs for security threats using Datadog's features.