Giving up drinking, particularly if you have drunk heavily, can bring many health benefits in the long run. However, in the short term it can cause mild to severe side-effects. This is largely because your body had adjusted to the presence of alcohol and is disrupted by its withdrawal.
The main reason people suffer short term ill-effects from giving up alcohol is tolerance. This is the body's ability to handle drinking without the immediate effects most people have from alcohol such as intoxication (it doesn't mean the body isn't harmed.) Although there is some evidence of genes playing a role in tolerance, it's also something that builds up the more you drink over time. One consequence of alcohol tolerance is that your body effectively comes to expect to have to process a certain amount of alcohol and thus is knocked "off-balance" when you stop drinking.
The withdrawal of alcohol from the body can cause unwanted symptoms in the short term. These include shaking and sweating a lot. You may feel sick or actually be sick. You may also get digestive problems such as constipation or diarrhoea. These symptoms usually get milder every day and should be gone within a week or so.
Giving up alcohol can disrupt your sleep patterns. This appears to be because alcohol makes you drowsy and your body gets used to falling asleep while intoxicated. Stopping drink may mean your body struggles to adjust to falling asleep "naturally" which can leave you feeling tired. It may even disrupt your sleep cycle such that you begin having very vivid dreams. The sleep disruption tends to last longer than the other symptoms but should eventually fade away as your body adjusts.
In rare but severe cases, you could suffer delirium tremens, known commonly as the DTs. The effects can be agitation and even hallucinations. This happens because alcohol can change chemical levels in your brain, so withdrawing alcohol can cause a short-term imbalance. If you suffer the DTs, you should seek immediate medical help as it can develop into a serious epilepsy-like seizure. If you have suffered the DTs in the past, you should get medical advice before trying to give up alcohol.