Then he said to her, “Daughter, your faith has made you whole. Go in peace.”Specifically, the questioner was wondering what was going on with the "faith has made you whole". After pointing out that the Greek suggests that her faith "saved" her and that most newer translations say that she has been made "well", this is what I had to say.
At that time, a Jewish understanding of "salvation" would hearken the listener back to the Exodus, which would've been the stereotypical example of "being saved". During the time of Jesus, Israel had returned from exile physically, but still seemed to have some sense of distance from God (for example, God never filled the Temple built by Herod the Great). Jesus' healings were in and of themselves allusions to what God's salvation really looks like (healing, renewal, restoration, new creation, etc..). Jesus is announcing the Kingdom of God, the rule of God, by pointing to the implications of what this means for the poor, the sick, etc... When he says your faith has "saved" you, he's obviously pointing out that she has been healed. But using the term "save" here implies that her healing is part of a much bigger project. This wasn't just her getting better, but is what God promised he would do all along, return and vindicate Israel and, through Israel, the world.