Surgery

Surgery is a medical procedure that consists of opening the patients body while he's sedated in order to make a modification. This can be taking something out, putting something in, replacing something,etc. This medical procedure first appeared as soon as in ancient Greece. There are different types of surgery, elective surgery which is for non life threatening diseases, amputation, and other surgery that take the name of the organ that is beeing operated on (like brain surgery). It's usually used to cure but of course video games have found other uses for it. 
The first idea for a game that comes to mind when talking about surgery is one where you play as a surgeon. These games usually demand dexterity and quickness, which is why they're usually found on the DS  or Wii. Popular games that let you play as a surgeon are found under the Trauma Center franchise that spans Wii and DS. The gameplay usually asks you to use different tools like scalpels and defibrilators to remove tumors and other viruses, where the game adds fictional sicknesses.  
Surgery can be used in other ways in games. It can be used as a plot device. A character can change his appearance thanks to surgery and the character creation screen is sometimes explained in a story as the result of surgery (for example Mass Effect 2 or Saints Row 2).  
In horror games, the ugly monsters that you fight may be a result of surgery. Crazy surgeons are common doing awful things like trying to kill the main character or creating abominations. Horror game's usually make you go through hospitals where you can see the results of surgery gone wrong (for example Bioshock) and sometimes you may even have to escape from a mad surgeon (for example Heavy Rain) that use tools like drills and rusty saws for their surgery.  
Surgery in games can take on different forms but one thing is for sure that there will be blood and lots of it. Games try to replicate the real act of surgery and it ain't for the faint of heart which is why it's often used to add to the scares in horror games.