A quantum filament is an astrophysical phenomenon which could be very hazardous to space vehicles. Quantum filaments can be hundreds of meters long, but have almost no mass, making them extremely difficult to detect.
In 2368, the USS Enterprise-D collided with two quantum filaments, causing major damage to the ship. The Enterprise-D computer registered a hull breach, and main power failed. In addition, the quantum resonance of the filament caused a polarity shift in the ship's antimatter containment fields, leading to a progressive degeneration in the fields, threatening the ship. Eventually, the crew was able to restore power and stabilize the containment fields.
Counselor Deanna Troi incorrectly assumed that a quantum filament had properties similar to a cosmic string. (TNG: "Disaster") Two years later, while considering taking the Bridge Officer's Test, she recalled the incident with Riker. She explained that although she had been overwhelmed at the time, she later missed the feeling of being in command that the experience allowed her. (TNG: "Thine Own Self")
From the Star Trek Encyclopedia, 4th ed., vol. 2, p. 195, "An early draft of "Disaster" had the ship colliding with an asteroid, but the writers, sensitive to scientific concerns that an asteroid would not cause the damage described in the script, "invented" the quantum filament. We're not entirely sure what a quantum filament is, but we do know it's not a cosmic string."