Moral development is simply what it sounds like: the development of a moral code or system over time. This process usually begins with young children in their homes; parents, by example and by stated principles, teach their children the difference between right and wrong behavior. Even more, they encourage their children to behave by these moral principles.
This moral code is most heavily influenced by parents and other family memebers at first; however, over time, other factors exert influence over children as they become teenagers and then adults. At school their teachers and peers often help shape the moral development of children and young people (which is why parents are often concerned about the friends their children spend time with outside of their homes).
As they mature, children are influenced by laws and other authorities in their lives, including religious entities. While peers generally exert a significant influence over morality for a time, most people, at some point, determine to decide for themselves what is right and acceptable behavior in civilized society. Obviously there are those who never develop a proper morality or perhaps any morality at all; however, for most people this is a process which begins almost at birth and happens over time.
How children are taught the rules of morality and how they are punished for breaking them will certainly impact their moral development; when they get older they will be faced with conflicting moral codes (determinations of what is right and wrong). In the end, individuals choose their morality based on what and how they are taught as well as by factors which influence them throughout their lives.
For a more specific discussion of moral development theories, see the eNotes link below.