Amazon Aurora is a fully managed relational database engine provided by AWS. It includes automated backups as a default feature. Aurora automatically backs up data to Amazon S3 and maintains a transaction log called the 'backtrack' for continuous backup. This functionality allows users to restore their database to a specific point in time or roll back to a previous state. The other options, Amazon S3, Amazon ElastiCache for Memcached, and Amazon Elastic File System (Amazon EFS), do not provide automated backups by default. Therefore, the correct answer is B, Amazon Aurora.