Methadone is a synthetic opioid agonist, with a long duration of action. Because it can stay in the body for up to and over a day, it is often used to detoxify those addicted to heroin, and/or other shorter-acting opiates or opioids. It is also used in pain management, albeit at far lower doses than those used to treat addiction (unless the patient became addicted as a result of pain-management).
In The Softer Side, House turns to methadone for pain-relief, and experiences a near-miraculous recovery, being able to walk on his wounded leg without support, and seeming much happier as a side-effect. However, the drug also causes House to pass out repeatedly, as well as impairing his judgement, and he switches back to Vicodin, choosing to endure the pain rather than make more mistakes.