I see on some violins there is something on the A and E strings between the tail peace and the bridge.
What is it called and what does it do?
I found a similar thing on the violins of the soloist in these videos. I don't know if these are different from the picture above:
(look at 4:20):
This one is only on the D string:
Here everybody has it on their instrument, violin, viola, cello (look at 7:59):