Alcohol affects many different parts of your body. Even if you drink it in small amounts, it still affects your body but not as noticeably as when you drink larger amounts more regularly.
As posters have correctly said it is a depressant, so counteracts any stimulants in your body. Alcohol depresses both your central nervous system and the dopamine receptors in your brain. Once you remove this depressant your central nervous system and dopamine receptors "wake up", resulting in vivid dreams, restlessness, bad sleep etc. Until you become used to the lack of depressant, which can take a long time, depending on how much and for how long you have been drinking.
Your liver recognises alcohol as a poison and will divert all its effort into removing alcohol from your body primarily, which kills off liver cells. The liver can regenerate to a certain extent but not if you regularly put it under a huge amount of stress. Vitamin B supplements can help with supporting your liver, particularly B6, B9 and B12. Vitamin B3 can help with brain function. A good Vitamin B complex will help anyone, who has given up alcohol, repair their body.
If you would like to do further reading, please research PAWS.
(To end on a cheerful note, there is also pancreatitis, cancer and damage to the immune system to consider.)