House Wiki

In medicine, a fellow is a physician who has completed a residency and is qualified as a specialist, but is training in a sub-specialty. A fellowship will last for at least one year, and for as many as three. The people who work for House are classified as fellows within Princeton-Plainsboro's medical training system.

Fellowships are scarce and competitive.  Only a fraction of residents will be able to find a fellowship.  

However, fellows are usually not paid as well as other beginning specialists, and often make less than family practice physicians in general practice, making little more than what a resident makes.  Moreover, fellowships are difficult and have a much higher failure rate than residencies. Fellows are given a high degree of responsibility and must develop skills outside the practice of medicine, such as the ability to deal appropriately with patients and taking on administrative tasks and even teaching duties. They may be assigned as an attending physician within their original speciality.

However, physicians who complete a fellowship are in very high demand.  They can usually obtain jobs at a teaching hospital, work as a department head, or go into a lucrative private practice with hospital privileges. They can act as an attending physician or as a consultant in their sub-speciality.

Fellowship at Wikipedia