Moral responsibility is the recognition that some of our actions are more free than others. One must be careful though when you use the term “free”, because ultimately all of our “free” actions are constrained to a degree. They are constrained by the environment and they are constrained by neurobiological factors. Nonetheless, if we are going to derive any useful definition out of “morality” and “responsibility” we must admit that to a certain extent we are able to consciously choose or act in some cases. Regardless of whether our choices are constrained by our evolutionary past or by the causal factors of the environment, some of are actions can be considered “more free” than others, and it is on these choices that should be held morally responsible.
For an example of what I mean by constrained free will, look at the case of someone being pushed from behind. This is the extreme case of determinism where we would not hold someone accountable for falling down because the inital push had enough momentum has to ensure that falling down was the only end result. It is only the cases where someone is not “fully constrained”, where they have conscious choice, that we would hold someone accountable. Now granted, any definition of freewill will certainly change as our understanding of the brain and consciousness evolve, but we must take into account the existence of intentionality if we are going to have any useful account at all. Thus, we have freewill due to the nature of our physical brains, but it is “softly determined” by certain environmental and neurobiological factors.