Well, it depends on how in depth of an answer you're looking for. In general, the human brain is strongly wired to look for "reward", typically through activation of the dopamine pathway. These are dopamine (DA) producing neurons that extend from the ventral tegmental area (VTA) to other areas of the brain like the nucleus accumbens (NAc) and the prefrontal cortex (PFC).
These DA pathways are generally activated by all sorts of "rewarding" stimuli that make you want them. Imagine anything that you anticipate, and that anticipation likely comes from DA. This could be food, sex, playing a videogame you've been looking forward to, the thought of a break from doing work, anything. It's a huge motivator and deeply ingrained in human biology.
Almost all addictive drugs increase activity of the DA pathway, whether by increasing DA production, decreasing DA degradation, or lots of other mechanisms. This leads to individuals strongly seeking the source of the reward (the drug).
Almost all addictive drugs act on the brain’s natural reward circuitry, changing the way you feel, act and behave as you become increasingly dependent on the substance of your choice. When you drink an alcoholic beverage, inject heroin, take prescription painkillers or snort cocaine, these substances alter the way your brain processes chemicals called neurotransmitters.
Each drug acts in a specific way to change the brain’s response to stimuli, but the end result is that the experience of using the substance is so pleasurable, relaxing or energizing that it triggers your internal reward system, making you want to repeat that experience again and again.
Over time, your brain gets used to the response, and you need more of the drug to achieve the same euphoric, hallucinogenic or sedating effects. By this time, you may be displaying addictive behavior like:
* Compulsively seeking the drug
* Continuing to use the drug even though it’s obviously causing harm to you or your loved ones
* Lying, stealing or doing other things that hurt your sense of integrity in order to get the drug
* Taking dangerous risks in order to obtain or use the drug
Blatantly stolen from the 3rd result of a Google search for "why are drugs addictive"