ShareGate Migrate is a client-side application that relies on SharePoint and Microsoft 365 APIs to perform tasks.
The server extension adds services to your on-premises SharePoint server(s) to expand the capabilities of the available Microsoft APIs.
It allows ShareGate Migrate to package your content for improved performance and to migrate content that would otherwise not be supported with these APIs.
The server extension's added services do not affect your SharePoint server's normal operations. It does nothing outside of a migration process.
ShareGate Migrate executes these server extension services in the context of a connected user and cannot perform tasks that the user would not be able to accomplish otherwise.
For more info on how ShareGate Migrate migrates SharePoint content, see SharePoint to SharePoint migration diagram.