AWS DataSync is a service that makes it easy to move large amounts of data online between on-premises storage and AWS storage services. AWS DataSync can transfer data at speeds up to 10 times faster than open-source tools by using a purpose-built network protocol and parallelizing data transfers. AWS DataSync also handles encryption, data integrity verification, and bandwidth optimization. To use AWS DataSync, users need to deploy a DataSync agent on their on-premises servers, which connects to the NFS servers and syncs the data to Amazon S3. Users can schedule periodic or one-time sync tasks and monitor the progress and status of the transfers.

The other options are not correct because they are either not cost-effective or not suitable for the use case. Setting up AWS Glue to copy the data from the on-premises servers to Amazon S3 is not cost-effective because AWS Glue is a serverless data integration service that is mainly used for extract, transform, and load (ETL) operations, not for simple data backup. Setting up an SFTP sync using AWS Transfer for SFTP to sync data from on premises to Amazon S3 is not cost-effective because AWS Transfer for SFTP is a fully managed service that provides secure file transfer using the SFTP protocol, which is more suitable for exchanging data with third parties than for backing up data. Setting up an AWS Direct Connect connection between the on-premises data center and a VPC, and copying the data to Amazon S3 is not cost-effective because AWS Direct Connect is a dedicated network connection between AWS and the on-premises location, which has high upfront costs and requires additional configuration.