External account mapping passthrough allows files and folders that have been shared with an external account/user (a user that is outside the company) to continue to be shared with that user. This is an feature of permission migration and can therefore only be used with connectors that support that feature.
Example scenario
Source: GSuite
Destination: O365
Job Type: Copy
The purpose of the job is to transfer the contents of Folder A from the source to Folder B on the destination. Within Folder A is a file that has been shared to a user outside of the organization, and it is desired to maintain that connection. Because "permission migration" is being utilized and "External account mapping passthrough" is enabled the external account will still be associated with the file after it has been transferred. Additionally if auditing is enabled the user name or email associated with the external account will be visible.