The MongoDB Backup tool allows developers to restore their database from a corrupt or lost state by using backups to start over. Before restoring, it's essential to configure the backup delivery method and ensure sufficient disk space on the machine receiving the backup files. Once restored, data can be retrieved from stored snapshots or point-in-time restores within the last 24 hours. Additionally, for sharded clusters, cluster checkpoints can be configured to enable restore functionality. The process involves retrieving snapshots from the Sharded Cluster Status page, selecting the replica set or shard to restore, and clicking on the "restore this snapshot" link to initiate the restoration process.