Amazon Kinesis is a managed service for processing and managing large data streams in the AWS cloud. It allows users to ingest, process, and distribute data to multiple consumers simultaneously. Monitoring key performance metrics such as incoming requests, outgoing requests, latency, iterator age, and shards per stream can help ensure that Kinesis is performing at its best. Additionally, custom tags can be applied to Kinesis streams to split, aggregate, or filter metrics, and Datadog offers alerting features to notify users of any abnormalities with Kinesis metrics. The integration allows users to track performance metrics in real-time, providing valuable insights into the health and performance of their Kinesis applications.