Docker Compose allows defining and running multi-container Docker applications. It uses a compose file to configure applications composed of multiple services that use Docker's API to start and stop containers together. Docker Swarm extends Docker's clustering capabilities and schedules containers across multiple Docker hosts. While Docker Compose is for single host deployment, Swarm enables scheduling containers across multiple hosts for scaling and high availability. The session covered Docker Compose configuration, networking, and compared it to Docker Swarm for clustering containers across multiple hosts.