What is the medical term meaning inability to eat?

The common medical symptom of loss of appetite is called "anorexia".

This is often confused by some people's use of the Word "Anorexia" to mean Anorexia Nervosa, which is a diagnosed condition with components requiring intervention in both medical and psychological disciplines. Sometimes you must determine by context which is being referenced.

Examples:

"Doctor, I'm just not feeling well, I'm not hungry and I get tired easily," said the woman.

"How long have you had this anorexia, and have you also had weight loss?" asked the doctor.

"My sister has finally accepted treatment for her Anorexia at a specialized treatment center for Anorexics, she is down to 88 pounds now."

"Our facility is specialized in the treatment of Anorexia Nervosa."

"Some of the early symptoms of clinical depression are: lack of interest in normal activities, hypersomnolence, anorexia (or increased appetite and binging), fatigue, and inattention to appearance and hygiene."

"Poor Bob was diagnosed with cancer. The first sign he had of anything wrong was when he began losing weight due to severe anorexia and nausea."

See the link below for more information about the symptom of anorexia and about the condition of Anorexia Nervosa.