My dad has stage 3 melamoma cancer they removed the area infected and took out the infected lymph nodes under his armpit. Why are they givign him chemo?

To cure him! Melanoma is a very aggressive cancer, sadly. Cancer cells leave the main cancer early and travel through the bloodstream. Even though your dad's cancer was removed surgically, those traveling cells must be killed. The only way to do this is with chemotherapy, which gets into every part of the body. His doc is trying to keep his melanoma from coming back! it's hard but it's what he needs.
Being thorough. I can't comment on the specific case. However melanomas are very aggressive cancers, and the oncologist may order chemotherapy as a safeguard to try to destroy any left over cancer cells that may not have have been removed surgically.
Standard of care. For stage 3 melanoma the standard therapy is to remove the main cancer & affected lymph nodes and then follow with chemotherapy (actually interferon Alpha which is a form of immunotherapy given for 1 year). This is done to reduce the likelihood of the cancer retruning and spreading to other areas. Sometimes radiation may also be given after surgery to the armpit.