Docker is a platform that uses images and containers to manage applications, where an image is the application itself, and a container is a running instance of that image. This relationship can be likened to a class and its instance in programming terms, where multiple containers can be created from the same image. To illustrate, the analogy of media formats is used: an image is like a VHS tape or a DVD, while the container is the player that runs it, such as a VCR or a DVD player. This metaphor helps simplify the understanding of how Docker images and containers function in different environments.