Kubernetes can be used to scale multi-tier applications by providing tools for container orchestration, including service discovery, load balancing, storage orchestration, and self-healing capabilities. It addresses challenges with traditional monolithic architectures by allowing microservices that are isolated, declarative, and can autoscale horizontally and vertically through features like horizontal pod autoscaling, vertical pod autoscaling, and cluster autoscaling. This allows applications to dynamically add or remove pods and nodes as needed to meet changing workload demands.