Adjuvant therapy is any treatment in addition to the primary, main, or initial treatment and can be given before, after or concurrent with the primary treatment. So for a given patient, chemo, radiation, or surgery, or other targeted therapies can be either primary or adjuvant.
Neoadjuvant treatments are given before the primary treatment for the purpose of improving the effectiveness of the primary treatment. In the case of cancer that usually means shrinking a tumor or preventing or limiting spread to other organs with chemotherapy. Those are the benefits. The risks are the side effects, which can be short term, long term, temporary, or permanent and depends on a whole range of variables such as the patients general health, type, stage, and aggressiveness of cancer, age, and many other lifestyle. You need to talk to your Dad's oncologist about the risks vs. benefits of additional chemotherapy prior to surgery, since each case is different.