I'll try to define it-

What does working through the transference mean? Experiencing, processing, discussing, and understanding the feelings brought about in the therapy relationship.
How do you know the work is done? The transference slowly dissolves and you relate to your therapist more like a therapist rather than the relationship that you need.

Only my attempt...

Without things being clouded by transference, you can relate to people as who they are rather than what you need them to by. It also helps define who you are-your sense of self-apart from all those unmet needs.