This is a piece of sticky webbing taken from an Arachnoid cocoon. You got it as a reminder of a tale you like to call:
It all started when Terrence Dobbs asked you to help clear Arachnoids out of an Arachnos research lab. You went in there and managed to rescue one of the research scientists, Doctor Weisen, who mentioned how Executioner Garrod had been taken by the Arachnoids.
Dobbs spoke with Arachnos, and they stated they wanted their soldier back. Dobbs sent you to speak with Regent Korol, who informed you how Arachnos tracked some of their more valuable assets through the use of implanted homing beacons, a little trick they picked up from Crey Industries. She gave you a tracking device to lead you right to where Executioner Garrod was taken.
You broke into the Arachnoid tunnels and found a number of people held captive in cocoons, presumably to be eaten! You managed to find Executioner Garrod in the end, freeing him from the webbed nightmare of the Arachnoids.