Docker is a containerization platform that provides a complete system for building and running software containers, which package applications and their dependencies as ephemeral units. The client-server driven architecture of Docker involves the CLI sending requests to the Docker daemon (dockerd), which exposes a REST API as a Unix socket or network interface. Key components include images, registries, runtimes, and containers. Docker's architecture allows for managing multiple hosts with a local CLI installation, building images remotely on powerful machines, connecting developers to shared environments, and automating container interactions using the REST API.