The modern usage of the phrase refers to a Christian tradition regarding Saint Peter. According to the apocryphalActs of Peter (Vercelli Acts XXXV), Peter is fleeing from likely crucifixion in Rome at the hands of the government, and along the road outside the city he meets a risenJesus. In the Latin translation, Peter asks Jesus "Quo vadis?", to which he replies, "Romam vado iterum crucifigi" ("I am going to Rome to be crucified again"). Peter thereby gains the courage to continue his ministry and returns to the city, to eventually be martyred by being crucified upside-down.
The phrase also occurs a few times in the Vulgate translation of the Bible, such as in John 13:36 when Peter asks Jesus the same question, to which he responds, "Whither I go, thou canst not follow me now; but thou shalt follow me."