The term [cancer] is Latin and means "crab". The word was first used by Galen of Pergamon (129AD - 200AD) who used it to describe the crab-like appearence of the veins of a cancerous tumor, probably a breast cancer. Galen said "... as a crab's feet extend from every part of its body, so in this disease are the veins distended, forming a similar figure". The term cancer is also used in other applications, such as astronomy (Tropic of Cancer) and astrology, as in the zodiacal sign of Cancer. 

The Latin term [cancer] was probably pronounced "kanker" and this may be the origin of the term [canker] to refer to ulcerations around the mouth or angles of the mouth, canker sores. This is also probably the origin of the term [chancre] used for some dried-out sore wounds. 

Greek terms merged into the New Latin, so the Greek terms derived from [karkinos] also made it into modern medical terminology.

    Colon cancer. Click on the image for a larger picture of a different cancer. WARNING: The larger image could be disturbing.

The accompanying image is that of a colon specimen with a cancerous tumor. If you click on the image a larger depiction of a cancer of the breast will appear. WARNING: This secondary image could be disturbing to some of our readers.

Sources
1. “A Dictionary of Medical Derivations" Casselman W. Parthenon Publishing, 1997
2. "The origin of Medical Terms: Skinner, 1970
3. "Cancer - Wikipedia"
Images courtesy of Wikipedia 

Personal note: This article is published in memory of my cousin Hugo Barahona who passed away on January 1st 2014 with a cancerous pathology. May he rest in peace. Dr. Miranda