Maxim Brown discusses the importance of monitoring an EKS cluster and provides various methods for accessing Kubernetes metrics, including Kubernetes-native methods, AWS CloudWatch, and a dedicated monitoring service. He explains how to use tools like `kubectl`, Kubernetes Dashboard, and AWS CLI to collect and visualize metrics from the cluster. He also highlights the limitations of these methods and introduces a dedicated monitoring service that can centralize all sources of data into one platform, providing a more complete picture of the EKS cluster's health and performance.