A brain transplant aka whole-body transplant is a surgical procedure in which the brain of one organism is transplanted into the body of another. It's separate from a head transplant, which would involve transplanting the entire head from one organism to another. Theoretically a brain transplant could be used to give an individual with advanced organ failure new life.
Historically, only one brain transplant has been conducted. This by neurosurgeon Robert J. White in the 1960s, who transplanted the brain of a dog into the neck of another dog. EEG readings showed the brain was later functioning normally. It also proved the brain was an immunologically privileged organ as the host's immune system did not attack it.
Brain Transplants have been the subject of various fictions which explore it's more malefic applications; such as using the procedure to give an infiltrator the identity of an individual who has been abducted. Other aspects explored in the realm of fiction involve Transhumanism; in which an individual achieves immortality though the procedure, and/or has their brain transplanted into a genetically superior body.