A carrier is an individual who has a disease organism living within or on their body, is able to pass on this disease to other persons (i.e. is contagious) but suffers no symptoms of the disease even after a lengthy period of time.
Carriers can be very dangerous individuals. Human beings are usually intelligent enough to avoid anyone who shows obvious symptoms of a life threatening disease. As a result, most diseases are often passed on during a disease's incubation period - when it is too weak to cause symptoms, but remains contagious.
However, carriers can provide a breeding ground for disease, occasionally for the natural lifespan of the carrier, without the symptoms ever becoming obvious or affecting the patient in any way. For reasons that are not fully understood, the disease is not eliminated by the immune system even though it can easily be detected in blood cultures. It is believed that many carriers merely have genetic quirks that both resist the effects of the disease yet don't recognize it as a foreign body.
One of the best known carriers was "Typhoid" Mary Malone, who worked as a cook and spread the disease to dozens of her employers before she was involuntarily committed to a hospital. She never showed the typical symptoms of typhus, such as life threatening diarrhea.