A sync coil is an essential component in a Colonial jump drive.
Galen Tyrol sabotages Felix Gaeta's attempt to jump Galactica and permanently fracture the Fleet by entering the FTL engine room and forcibly removing the sync coil, disabling the entire jump system (TRS: "Blood on the Scales").
After the mutiny is over, Tyrol tells Admiral William Adama that he later discovered serious structural damage to the battlestar's superstructure after he removed the sync coil (TRS: "No Exit").