Garage doors use a variety of systems of counterbalance and force to open. In the case of a torsion spring counterbalance, there are two springs which are very tightly wound, surrounding a long steel shaft, each with what's called a cable drum at each end. The whole system, which is quite complicated, goes above the garage door along what's known s the header wall. The contraption has three main support structures- a steel or nylon bearing plate in the center and then two other bearing plates, each at each end.
Torsion spring garage doors use steel wire with a stationary cone, which is attached to the center bearing plate, and a winding cone at the other end with holes at four 'corners' which allow it to be secured to the shaft.
Counterbalance cables along the roller brackets are generally made of steel. They go at the bottom corners of the garage door in order to allow the cable drums to properly 'click' in.
When you lower your garage door, the cables slowly unwind and unwrap from the previously mentioned drums, and the springs are pressed/wound back into their full tension mode.
The whole system relies on very precise, delicate physics that could take a good hour and a physics or mechanical engineering degree to explain.