Columbus wanted to find a better route to the Indies by sea. After looking for sponsors for this quest he had King Ferdinand and Queen Isabella from Spain sponsor his trip. They requested that if Columbus succeeded in his venture he would spread Christianity, as well as bringing back gold and glory for Spain.
Columbus was also eager to spread Christianity to any land he reached. So the reason for setting up the cross when they arrived to America was to start spreading out Christianity specially since this was one of the reasons his trip was sponsored by the Queen and King of Spain.