In medicine, a disease is considered asymptomatic if a patient is a carrier for a disease or infection but experiences no symptoms.
A condition might be asymptomatic if it fails to show the noticeable symptoms with which it is usually associated. Asymptomatic infections are also called subclinical infections.
Other diseases (such as mental illnesses) might be considered subclinical if they present some but not all of the symptoms required for a clinical diagnosis. The term clinically silent is also used.

Many cancers can develop and grow without causing symptoms, especially in the early stages.
The primary emphasis for asymptomatic cancers is to focus on screening and early detection. Although some cancers can remain asymptomatic for long periods of time, almost all cancers cause little to no symptoms in the earliest stages of disease.

Examples of cancers that may cause few or no symptoms include:
Cancer of the tail of the pancreas
Early stage breast cancer
Early stage colon cancer
Kidney cancer
Lung cancer
Ovarian cancer

Adapted from (1) Wikipedia, the free encyclopedia and (2) American Cancer Society. Cancer glossary. Internet. Accessed on May 23, 2016.