Necessary to run main engine of the ship, including the grav thrust, power plant, and life support. Obviously, a compression coil would be an integral piece of a Trace Compression Block engine such as the one that the Firefly Transport uses. Part of the Compression Coil, the Catalyzer, blows in the episode Out Of Gas. Being as Kaylee said it was the port one, there is likely a starboard one also, although it appears the Compression Coil rotates as part of the main engine.
Kaylee mentions in the first episode that they need a new compression coil; apparently this is foreshadowing.