A Pod can contain multiple containers, but for the most portion of the situations, it makes perfect sense for the Pod to be simply an abstraction over a single running container.

In what situations does it make sense to have a multi-container deployed Pod?

What comes to my mind are the scenarios where you have a primary Pod running, but you need to tightly couple helper processes, such as a log watcher. In those situations, it makes perfect sense to actually have multiple containers running inside a single pod.

Another big example that comes to my mind is from the Istio project, which is a platform made to connect, manage and secure microservices and is generally referred as a Service Mesh.

A huge part of what it does and is able to accomplish to provide a greater control and customization over the deployed microservices network, is due to the fact that it deploys a sidecar proxy, denominated Envoy, throughout the environment intercepting all network communication between microservices.

Here, you can check an example of load balancing in a Istio service mesh. As you can see the Proxy is deployed inside the Pod, intercepting all communication that goes through it.