The Gamow peak is a peak in the probability that atoms moving at some speed within a gas will fuse, i.e., that fusion will take place. It is a factor in nucleosynthesis, such as fusion within stars. The probability, called the Gamow factor, is the combination of two probabilities: the probability that two atoms will a particular relative speed (based on the Maxwell-Boltzmann distribution), and the probability of quantum tunneling given that relative speed, a probability that quantum mechanics provides. Fusion primarily takes place through quantum tunneling of a particle through the electric field of another (repelled by the Coulomb force), to get sufficiently close that the strong force holds them together.
The Gamow factor and Gamow peak of a gas are dependent upon its temperature as well as its constituents. Tunneling is more likely with higher the speed, but at a given temperature, there are fewer atoms as you consider higher speeds, and the combination of the two probability distributions features a maximum probability of tunneling, the Gamow peak. The Gamow window refers to a general range around the peak within which the majority of the fusion will take place.