To explain, quantum mechanics refer to the behaviors of particles, which work differently than large scale physics predicts. The most important aspect to this discussion is particles behaving differently when measured vs not measured. Light for example is a wave when not measured, and a particle when measured. The photons, before being measured, act as a wave becaue their values are not defined before measurement (or observation). This is the source of true randomness in the universe. Theoretically, you could predict the behaviors of anything in large scale physics by having the starting conditions. Quantum mechanics do not allow you to predict the future even with the starting conditions.

Since our brains are essentially quantum computers, it can not be claimed that our choices are pre-determined. This does not prove free will beyond a reasonable doubt, (randomness being involved in our decision does not entirely disprove the notion that our decision is just a mechanical process) but it is a very strong argument for free will because it at least contradicts the notion that everything that we choose is pre-determined by the starting conditions in a system.