As the protons move down their concentration gradient in the electron transport chain, what's happening with the electrons in the chain?

The protons move from matrix into the inter-membrane space, at this spot the electrons are actually moving down from area of high energy to the area of low energy, thereby releasing energy in its impact. And this energy is used to pump those protons. As protons move towards the inter-membrane space, thus there will be more positive charge due to accumulation of protons.

The gradient formed can also be used to make up ATP. As the protons move down the gradient and then into the matrix, there they come up with an enzyme called ATP synthase, this ATP synthase is use its energy to make ATP. The number of ATP produced is directly proportional to the number of protons that are pumped.