Man Friday is used as an idiom. It refers to a very loyal servant or his master’s right hand man. Nowadays it is more than that. He is the person who is most efficient and helps his seniors to complete the difficult tasks on time and rescues the Boss from embarrassing situations.
He is one of the main characters in the book Robinson Crusoe written by Daniel Defoe. In this novel, Robinson Crusoe spends many years on an island near Venezuela. He chances upon the custom of cannibalism in which this man was to be killed. Crusoe rescues him and the man becomes indebted to him for whole of his life.
Since this happened on Friday and Crusoe did not understand the language of the man, he names him as Friday. He remained with him for rest of his life and took part in the rescue of many more victims.