Any surgical procedure that is considered routine and low risk enough that the patient can be prepped, administered the procedure, and released from recovery in a very short amount of time (usually no longer than one day).
Both medically necessary and cosmetic surgeries can be lumped into this category; breast augmentation, LASIK eye surgery, appendectomies, and lots more are easily done with a quick, half day visit to your friendly local surgeon.
The ease of performing plastic surgery of all kinds on an outpatient basis has undoubtedly contributed to its appeal and popularity; if it took a week of inpatient surgery to make breasts bigger, nobody would bother.
Outpatient surgery differs from inpatient surgery in that a lengthy hospital stay is not expected. Normally only patients in otherwise good health are even considered for outpatient surgery; if any risk of secondary infection or other complications is present, it's inpatient for you. Outpatient surgery can still put you in the hospital if the shit hits the fan.
Outpatient surgery is routinely performed in a regular, boring office building. Minimal sterilization of the office is needed (outpatient surgery is sometimes performed in the physician's office, rather than in a surgery theater), and local anesthetic is prevalent (general anesthesia is generally reserved for inpatient surgery). It is significantly less expensive than inpatient surgery, as only one or two nurses, and the physican, are involved. In a hospital, you've got room and board, lots of nurses and orderlies, the operating room and its associated costs, bad hospital food, and more.