I found the article written by J. A. Brewer, “Craving to quit: Psychological models and neurobiological mechanisms of mindfulness training as treatments for addictions,” to contain a useful description of addiction and craving.
One of the contributing factors to addiction is the formation of associative memories between the addiction and positive and negative affective states. A smoker remembers that smoking when stressed helps him to relax, and that when he doesn’t smoke he feels stressed, so he is likely to keep smoking. This in turn forms an addictive loop in which the smoker becomes stuck.
Craving is the urge to act on the desire for the addiction. When a smoker hasn’t smoked in a while, he will begin to actively seek out a cigarette and will not feel like himself until after he has smoked. However, it is important to note that craving is not a response to the object of addiction; rather, it is a response to the affective tone that accompanies the perceptual representation of the sensory object. Craving is not about the actual cigarettes, it is about the feelings that accompany the cigarettes.