Everyone has an "inner child" whether they consider it such or not. It is the part of you that just wants to be safe, feel loved, and have fun. It is also the part of you that wants to scream and throw things like a 4-yr-old when life isn't safe, loving or fun. (Or at least I do! :-P)
Many people who were hurt when they were young children carry that hurt inside of them still. Many did not get the love that they needed as children; the environment they were raised in was unsafe or abusive. Sometimes they feel mentally split, dissociating themselves from their own past so as to distance the pain. When this happens, the "inner child" can take on its own form or seem like a seperate person. Regardless of whether he or she feels like a seperate person, however, it is still possible to use inner child work to heal the hurt that your past self experienced.
Inner child healing is different things to different people. It can mean trying to contact that little person that you have dissociated from, or it can simply mean treating yourself kinder and forgiving yourself for what happened to you. (We can tell ourselves that it wasn't our fault but the irrational 4-yr-old doesn't always believe that or feel that way). Some people find writing or talking to themselves helpful. Others use meditation. Still others simply do things for themselves that a little child would enjoy, such as swinging on the swings or blowing bubbles. Either way, inner child work is about letting that part of your mind and spirit feel safe, loved, and well.
This is a short article explaining Inner Child Healing:
http://healing.about.com/od/innerchild/a/soothinnerchild.htm