Fundoplication is the surgical method used to correct GERD - GastroEsophageal Reflux Disease (aka really bad heartburn). The name comes from the anatomical part used (the fundus of the stomach) and the technique (plication, the gathering, wrapping, and suturing in place of said part). The most common method, to my knowledge, is the Nissen fundoplication, which may be performed either laparoscopically or through an abdominal incision or laparotomy.
One of the more common reasons for GERD is laxity of the lower esophageal sphincter, which allows gastric juices (which, essentially, are hydrochloric acid) to leak out of the stomach and up into the esophagus, causing severe pain, burning, and frequently contributing to asthma. This is what fundoplication is designed to correct.
During the operation, the surgeon frees the base of the esophagus from the diaphragm and the ligaments that keep it from bouncing about as you move. He then uses the fundus to basically tighten the lower esophageal sphincter by wrapping it around the base of the esophagus and suturing it in place. If a full 360 degree wrap is used, the procedure is a Nissen fundoplication; if a partial wrap is performed (such as for some patients with esophageal motility problems, i.e. swallowing difficulties, it is a Toupet fundoplication
If the patients are screened to ensure that sphincter laxity is, indeed, the cause of their GERD, fundoplication has a 95% success rate. Complications include hemorrhage, infection, and food becoming lodged in the esophagus due to too-tight wrapping. This can generally be corrected endoscopically, by using a series of lead-weighted dilators to stretch the sphincter opening.