Addiction describes a condition where a person becomes psychologically (and sometimes physically) dependent on a drug. In addition to opioids, illicit drugs and other pharmaceuticals such as amphetamines, barbituates or benzodiazepine can be addictive, as can other substances such as nicotine and alcohol.
Once a person becomes addicted, trying to quit the drug becomes very difficult as the body goes through physical withdrawal symptoms which lead to cravings which can overwhelm the ability to focus on other tasks. Withdrawal symptoms can include nausea, fever, sensitivity to touch and light, insomnia, heightened awareness and many others.
Modern treatment notes that many of the side effects of drug use are not due to the drugs themselves, but (particularly with illicit drugs) the delivery mechanism. For example, nicotine itself is fairly harmless, but other substances in cigarettes are far more harmful to the lungs. With heroin and cocaine, it is the substances the drug is "cut" with. However, the effect of other drugs, such as methamphetamine, can be dehabilitating no matter what the purity. As such, in many cases, patients are kept on a dose of a drug that satisfies their craving, such as the use of nicotine patches or nicotine gum, or methadone and buprenorphine for heroin addicts.
It is important to distinguish between addiction and physical dependence and tolerance. House mostly appears to have a drug dependence, but has not shown much evidence that he is an addict. The shows writers appear to not know the difference between the two. House shows symptoms of pseudoaddiction when his pain is uncontrolled.