Docker secrets provide a secure way to store sensitive information such as passwords, private keys, and API keys in a Docker swarm mode cluster. This approach ensures the immutability of sensitive data by encrypting it across all manager nodes and distributing it to containers associated with relevant services. Docker secrets are encrypted and can be accessed only by individuals with the vault key, which is assigned to service nodes that require access to the information. The secrets can contain various types of data but have a maximum size limit of 500 KB. Docker swarm mode is required for using Docker secrets, and they work in conjunction with services to orchestrate containers across multiple hosts. By utilizing Docker secrets, developers can enhance the security of their containerized applications by storing sensitive information securely.