What is immunosuppression? Why would one use it?
Immunosuppression is not used in cancer, in fact it is typically harmful unless of course the cancer is a immune or white blood cell cancer where suppressing their growth may be helpful. What you are perhaps alluding to is that an adverse effect of cytotoxic chemotherapy used in the medical treatment of cancer can cause immunosuppression. 

Immunosuppression is helpful when it is causing more harm than good. The immune system is powerful and sometimes when its fighting an infection it can go a little overboard and cause enough damage to harm someone in the long term. In this case immunosuppression is helpful in preventing too high a response. For example in an organ transplant the recipient's immune system may destroy the new organ, but immunosuppression can prevent rejection. 

Another case is when there is an autoimmune or inflammatory condition occurring. Rheumatoid arthritis being an example of the former and asthma being an example of the latter. In these diseases inflammation due to the immune system perhaps targeting our own body cells causes damage to our organs or cells and causes the disease. Immunosuppression here can limit or prevent further degradation or sometimes even reverse damage due to inappropriate immune responses. 

Interestingly the human body must keep a good balance between being under and overactive. Certain individuals with better ability to control HIV infections or other infections are genetically more likely to also get autoimmune conditions.