Introduction: All lifts contain at least two phases: the concentric and eccentric phase. The concentric phase occurs when the muscle contracts to complete the movement while the eccentric phase occurs when the muscles relax to get back to the starting position. Generally speaking, the concentric phase is where the muscle does most of the work; however, focusing on the eccentric phase remains a very important part of each exercise for numerous reasons.
On the left, I have drawn a free body diagram of a preacher curl. In this case, the eccentric phase of the lift would be lower the barbell back down. Given this, the forces acting upon the bar to move it down would solely be gravity. This means that if we were to let the bar go, it would accelerate downwards at a rate of 9.8 m/s. Thus, in order to move the bar down at a constant, controlled rate, the biceps would actually have to CONTRACT in order to counteract the gravitational force. This means that the muscles spend more time under tension which causes more microscopic damage to the muscle fibers, leading to more hypertrophy.
Also, controlling the eccentric phase of a lift reduces the risk of injury. In the same example with preacher curls, if we were to just let the barbell go, we risk injuring the connective tissues in our arms because a high tensile force is being applied to those connective tissues over a short period of time. The connective tissues may not have time to adapt to the sudden change in force dynamics leading to strain or injury.