The force to restore the balance wheel is what the hair spring creates. There must be a restoring force to enable isochronal oscillations. A hair spring is a flat spiral that moves when the balance wheel vibrates. Through time, material for hair spring is changing. Some prefer steel or gold and some also vie for temperature resistant alloys or even silicon.
A mechanical watch is relying so much on the hairspring and the balance wheel. These two act as the regulating organ to accurately keep track of time. It serves as a harmonic oscillator that resists external disturbances for maximum accuracy. In a clock, the balance wheel and hairspring are like a pendulum. Balance wheel and hairspring are more suitable to a watch because it is portable while the pendulum is not.
Featured Image Credit: Revolution.Watch