It can be a swollen lymph node due to some local infection or skin injury, infection of the lymph node it self, or it may be swollen lymph node due to breast cancer or even, due to a cancer of lymphatic tissue or lymphoma.
Women should always visit their physician when noticing a swollen lymph node under the armpit, since the breast cancer can appear first in armpit lymph nodes and then in the breast tissue it self.

Your mother should visit her physician!