Docker Swarm makes it easy to distribute your apps across multiple machines. It offers the advantages of Kubernetes (simple scaling through dynamic clusters, reliability, etc.) but is less complex to use and operate.
Docker Swarm stacks are configured using simple YAML files, similar to docker-compose. Porting a docker-compose project to Docker Swarm is trivial in practice; the concepts are similar and you get the advantages of a cluster system without much additional effort or changes.