Very good question...I watch a lot of TV medical shows and still did not know exactly what it meant...here is an explanation I found on Wiki --- good luck!
Residency is a stage of graduate medical training. A resident or house officer is a physician (holding either a M.D., D.O., or MBBS, MBChB, BMed degree) who practices medicine usually in a hospital or clinic. The definition of residency varies worldwide by country and structure of the medical industry. In the US, it is classically associated with physicians (M.D. or D.O.). The training programs of allied health professionals may also involve a period of training termed "residency." This includes pharmacists, physical therapists, physician assistants, veterinarians, podiatrists, medical physicists, optometrists, and dentists.
A residency may follow the internship year or include the internship year as the first year of residency. The residency can also be followed by a fellowship, during which the physician is trained in a specialty or a sub-specialty. Successful completion of residency training is a requirement to practice medicine in many jurisdictions.
Whereas medical school teaches physicians a broad range of medical knowledge, basic clinical skills, and supervised experience practicing medicine in a variety of fields, medical residency gives in-depth training within a specific branch of medicine. A physician may choose a residency in anesthesiology, ophthalmology, dermatology, emergency medicine, family medicine, internal medicine, neurology, obstetrics and gynecology, otolaryngology, pathology, pediatrics, plastic and reconstructive surgery, psychiatry, physical medicine and rehabilitation, radiology, radiation oncology, neurosurgery, Oral and Maxillofacial Surgery, surgery, or other specialties.