Immunosuppressant drugs are simply drugs which suppress the immune system. In other words, they reduce the effect of the tiny germs that protect your body from dangerous germs. This makes the body open to disease but it is useful in other ways:
When someone receives an organ transplant, the body thinks the new organ is dangerous and tries to get rid of it. This is called organ rejection. If immunosuppressant drugs are taken the body usually accepts the new organ.