Piece of wire as FM antenna
The lump at the end of the wire is probably just a weight intended to keep it hanging straighter than it would on its own.

When you grab the end of it, you're coupling your own body capacitance to the end of the antenna, increasing its effective length/area and therefore its sensitivity, producing better "quieting" in the receiver.

One way to replicate this effect would be to take one or more alligator clip jumper leads and connect them to the end of the existing antenna wire (just before it enters the lump) in order to lengthen it. Try to squeeze the jaws so that they cut through the insulation and make contact with the conductor inside.

You can clip the other end of the jumper to something convenient on the wall (e.g., curtains or blinds) in order to raise the antenna up in the air and further improve its sensitivity.