The bent metal plate is kept under the quilt, protecting your finger as you push the needle back up again. (The pic above shows the back of the quilt shown in the first pic) I suppose this method is related to spoon quilting, which I have yet to try. In the beginning, learning to quilt this way I felt like a beginner again. Some hours learning again had to be invested. I find it was worth it. Being able to quilt for a considerably longer time at a time, without pain and fingers with calluses, I find amazing. Also I like my stitches, and think they show better on the back of my quilts. Another great plus is that it is not exaggerated to say that the quilting is more time efficient. I love the process of quilting, and do not care if things take a long time, but quilting this way allows me to handle more UFOs.
Jean Brown's demonstration of the technique can be found here. I appreciate that we all have our own preferred methods. This is just one happy quilter's ramblings... And I do not know Jean Brown, but I am grateful to her for showing a great way of avoiding sore fingers when I get to do what gives me much pleasure.