Docker Swarm allows managing multiple Docker hosts as a single virtual Docker engine. The presenter demonstrates setting up a traditional Docker Swarm cluster with an external key-value store and load balancer. SwarmKit provides the core components of Docker Swarm as standalone binaries. Docker Swarm Mode is integrated directly into Docker Engine 1.12 and later, providing built-in orchestration without external components. The presenter then demonstrates a tutorial using Docker Swarm Mode to deploy a multi-container voting application across 3 Docker hosts and scale the service.