Well, headers are the pipes that remove the combusted mixture (ideally Water + CO2) and sends it out of the vehicle...
I dont claim to know too much but what i do know is that a larger pipe coming out of the motor means better flow and better flow in turn results in increased horsepower and torque (what we want)
has 2 diff. types available, i dont know what i'd pick... i believe they are designated as 'racing' headers but do your research as i do not know how it will affect your warranty or other factors on your tC.
Oh and if you replace the header, might as well go for a full exhaust upgrade too... your car is only as strong as its weakest link.