The Gamow peak is the peak of the probability density function (PDF) that relates the probability of fusing to the speed of atoms within a gas; atoms moving at the speed indicated by the peak are those most likely to undergo fusion. It is relevant to nucleosynthesis by fusion, such as that within stars. The probability of fusing, called the Gamow factor, is the combination of two probabilities: the probability that two colliding atoms will have a particular speed relative to each other (assuming 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.