Docker Swarm commands are used to manage and orchestrate a cluster of Docker nodes. These commands include initializing a Swarm with 'docker swarm init', joining nodes to the Swarm with 'docker swarm join', listing nodes with 'docker node ls', and managing nodes by promoting or demoting them using 'docker node promote' and 'docker node demote'. Other commands involve deploying services, creating overlay networks, and scaling services within the Swarm cluster. These commands help streamline the process of managing containers and services in a distributed environment.