Datadog provides a comprehensive PostgreSQL RDS monitoring solution that integrates with Amazon RDS and allows users to collect key metrics, query metrics directly from the database, and gain visibility into application-level performance. The integration also enables users to set up distributed tracing and APM to monitor requests to their application and forward to Datadog, providing detailed insights into system performance. With this solution, users can create custom dashboards that combine key metrics from all sources, set up alerts for potential issues, and leverage machine learning-powered features like forecasting and anomaly detection to identify potential problems before they impact users.