Gamma rays are bursts of high energy light. Like UV in sunlight they essentially cause a form of sunburn. They are very difficult to protect you from – even 9 mm thick lead only cuts the radiation down to 25-50 %.
Gamma rays and their cousins X-rays are not very damaging to DNA, but because they are so difficult to stop it’s possible to target them to a tumour from outside the body. This is radiotherapy; essentially it’s a ray gun which is focussed on the tumour. Unfortunately healthy tissue is often in the way and gets damaged as well, hence the side-effects. Nevertheless, radiotherapy is a leading technique for curing cancer.
Gamma rays often don’t cause very much damage and they often have to be used repeatedly to kill a tumour. This site will also help you to understand how cells try to repair damage.