Even if you have a platform to run and manage your applications on top of Kubernetes, knowing how it works can be very beneficial when making design decisions in your code. For example, knowing what Kubernetes does when shutting down a container, or how storage is presented to the container. The better knowledge of the tools that you have at your disposal, the better you can use them.
Core Kubernetes does not concern itself with storage integration. At most, it provides a set of APIs, Persistent Volumes, Persistent Volume Claims, and Storage Classes. By default, containers can use their own ephemeral storage system and/or leverage host storage. Both of these solutions are typically inadequate for enterprise workloads. Ephemeral storage goes away if the container dies. Host storage ties the container to a specific host and (depending on how you access host storage) it can be insecure in multi-tenant environments.