Speaking in my own case, as someone who had a serious heroin habit (about 2 grams a day, which is a lot given an opiate-naive individual could get high off 2.5 milligrams), it works on two levels.
The first is the physical addiction; when you're taking heroin everyday, after around 3 weeks you become physically addicted to it. That means if you go around 24 hours without taking it, you go into "withdrawals". When you're in withdrawal, it's like having a really bad cold, you sweat a lot, you shiver, you find it impossible to get comfortable, when you lie down your legs ache, it's very hard to get to sleep. On top of that, you feel mentally very low, very anxious, a bit fragile overall. All of this is compounded by the fact that you know that a small hit of heroin you will immediately feel better; all the physical withdrawal symptoms disappear, and if it is indeed a small hit, then you will feel normal rather than the depression, anxiety etc described above.
The second level is that of psychological addiction. Taking heroin is like being wrapped in cotton wool, feeling completely safe, completely sufficient, completely whole in every way. Opiates like heroin are used as painkillers for physical pain, but interestingly they are also very effective for mental pain/discomfort/anxiety etc. That leads me to believe that there are perhaps some physiological/neurological similarities between how the brain processes the two distinct types of suffering.
When you take heroin, the first feeling is a euphoric rush, but it's not a rush in the sense of extreme stimulation (like 10 cups of coffee). It's a rush more like an orgasm, a feeling of exquisite satisfaction but also feels physical as well, because you can taste it (as the heroin moves through your bloodstream, it will pass through blood vessels in your nose and tongue, so you really can taste it). After a couple of minutes the feeling then becomes a very mellow feeling as described above; like being wrapped in cotton wool, feeling safe and whole. You feel quite drowsy, and can nod off quite easily. You also have very vivid dreams in those "nods" (these dreams were Samuel Taylor Coleridge's inspiration for his poem Kubla Khan, and also described in Thomas de Quincey's Confessions of an English Opium Eater).
I'm not addicted at the moment, I was coming up to exams and wanted to be as clear-minded as possible particularly as it was for land law (I got a 71, so I'm happy). Since then I haven't started again, and I'm prescribed a drug that blocks any cravings (Subutex). But I wouldn't say it's completely unlikely I would use again. I really enjoy opiates, unlike alcohol or cocaine they are not inherently damaging to the body (in fact, some doctors believe it may slow down aging as all of your metabolic processes slow down); it's not neurotoxic (kills brain cells) or cause cell death. The main health problems associated with opiates are when people inject it, with blood borne viruses from that, or when they spend all their money on heroin and don't eat properly, don't exercise, etc