There are multiple definitions for addiction. The simplest definition is physically and/or mentally dependent on a particular substance or activity. A quick search of the web will return multiple perspectives on the subject. You can find documents from renowned clinics and clinicians, as well as lesser known therapists and solution providers. The types of addictions run the gambit of human behavior. Some of the more common additions that are easily researched are: substance (drugs, alcohol, food) and activity (gambling, shopping, sex). Some researches use the terms substance and behavioral (instead of activity), but it would appear even some substance use can be attributed to behavior.
It is believed that some, both substance and activity, addictions are the result of self-medication. In those cases it is thought that the addition compensates for a treatment to an underlying disorder not be handled through other means. The underlying disorder may be physical or mental. Just as easily an addition may have started as recreational, and the physical or mental need resulted from the substance or activity fulfilling something otherwise missing. Then there are some substances that are addictive by nature. It is less likely that a person intended to or started out with the goal of becoming addicted to a substance or activity, but anything is possible.
It is also believed that some people are predisposed to developing addictions due to an addictive personality. Like most theories addictive personality has proponents and opponents. Would being predisposed to addition be an illness? Is addiction an illness? Again there are both proponents and opponents to the question of addiction and illness. While it is agreed, to some extent, that both mental and physical illnesses accompany addictions, there are some disagreements as to which came first the chicken or the egg. It can also be argued that the answer has to be determined case by case.