CSI is the container storage interface. It is a plugin for Kubernetes and other container orchestrators that allows storage suppliers to expose their products to containerised applications as persistent storage. You can look the detailed specification here.
Although prior to CSI Kubernetes provided a powerful volume plugin system, it was challenging to add support for new volume plugins to Kubernetes: volume plugins were “in-tree” meaning their code was part of the core Kubernetes code and shipped with the core Kubernetes binaries—vendors wanting to add support for their storage system to Kubernetes (or even fix a bug in an existing volume plugin) were forced to align with the Kubernetes release process.
CSI was developed as a standard for exposing arbitrary block and file storage storage systems to containerized workloads on Container Orchestration Systems (COs) like Kubernetes. Using CSI, third-party storage providers can write and deploy plugins exposing new storage systems in Kubernetes without ever having to touch the core Kubernetes code.