This idiom is often used in the context of war, when the bodies of soldiers who have died in battle are exhumed and identified so that their families can receive closure. In this context, giving faces to the lost means to restore the identities of those who have been forgotten.
This phrase can also be used in a more general sense to mean bringing attention to people or issues that have been overlooked or forgotten. For example, a filmmaker who documents the lives of people who live in poverty could be said to be giving faces to the lost.