The Lambda Telemetry API is a new local endpoint that allows Lambda extensions to receive telemetry data, including function logs, extension logs, events, metrics, and traces. It replaces the existing Logs API and provides backward compatibility. The API enables vendors to build better tools by giving them access to the Lambda execution environment, simplifying the process of forwarding logs to third-party log aggregation tools. The Telemetry API also provides additional features, such as detecting Lambda timeouts and auto-capturing them as CloudWatch metrics, which can be used to gain observability into complex serverless applications and troubleshoot issues.