Could you tell me if the axillary lymph nodes are removed, why would the arm be edematous?

Blocks lymphatics. The lymph nodes are accumulations of white blood cells which filter the extracellular water being carried back to the blood steam from all over the body. If the nodes are mechanically removed the lymph channels are no longer connected resulting in accumulation of extracellular water (edema) upstream from the removed nodes. Please see question 750811 for more details.
Blockage/narrowing. Lymphedema occurs when there is a compromise of the lymphatic circulation. This third circulation (arteries, veins) carries things too thick to be safely carried in arteries and veins like bacteria eaten by white cells and digested food. It is propelled along by normal body movements but contains a thick material called lymph. Blockage causes it to back up causing soft tissues/skin deformity.