I think it holds the finish plate on. Look at the base plate you see the bump outs clip may go in there. Then push over it a snap down to hold the finish in the lower notch.
This seems to be the solution, so far. (I will know for sure, once it's on the door). The little (moveable) tab that holds the finishing plate on bottom is holding the retaining clip, with gravity keeping it down. Both finishing plate and door knob seem secure. Somehow, I pictured this in a tighter area when I took it off a month ago.
Another lesson I learned. Take photos when disassembling. I had originally planned to replace the door knob so saw no need to. It would've been too difficult of a project to replace. And I didn't want to end up getting an entire new door if I couldn't find an exact match or didn't measure a for new one's location properly.
Also, I was "almost 100% sure" the clip went on the front of that silver back plate with the finishing plate in front of it. It looks like I was 100% wrong.