There are several possible Kubernetes services that you could find exposed on the Internet (or inside internal networks). If you find them you know there is Kubernetes environment in there.
Depending on the configuration and your privileges you might be able to abuse that environment, for more information:
You might have managed to compromise user credentials, a user token or some service account token. You can use it to talk to the Kubernetes API service and try to enumerate it to learn more about it:
Another important details about enumeration and Kubernetes permissions abuse is the Kubernetes Role-Based Access Control (RBAC). If you want to abuse permissions, you first should read about it here:
If you have compromised a K8s account or a pod, you might be able able to move to other clouds. This is because in clouds like AWS or GCP is possible to give a K8s SA permissions over the cloud.