The word exorcise derives from the Greek word exorkizein, meaning to drive out an evil spirit by invoking holy names. That’s still how we generally use the term exorcise today. But Ligarius is using the word in another sense, which we no longer use. In Shakespeare’s time, to exorcise also meant to conjure up the spirit of the dead in order to communicate with it. Ligarius is saying that he was almost dead from illness, but that Brutus has brought his spirit back to life.