In the Protestant Christian context of The Pilgrim's Progress, Christian is a heroic figure because of his willingness to undertake the journey to the Celestial City. He goes against the advice and wishes of both family and community, which are no small temptations. The journey is often lonely, violent, and rough, yet Christian has the courage to take it. His faith makes him heroic.
This is quite different from more traditional forms of heroism seen in classic Greco-Roman literature, which emphasize physical strength and cunning. Even in terms of individual action, Christian is often buoyed by outside aid, such as when the Evangelist redirects him to the path towards the Wicket Gate or when he gains armor and weapons for his battle with Apollyon from the Palace Beautiful. In fact, the allegorical nature of Christian's everyman role prevents him from emerging as a distinct individual. His heroism is therefore an ideal for the (presumably Protestant) audience to imitate. This is also the case within the text itself, such as when travelers see the monument to Christian's battle with Apollyon in the Valley of Humiliation. His triumphs give them hope that they too can face trials and overcome them.
Christian's heroic qualities aid him in his journey because he faces a great deal of persecution and hardship that might convince him the end goal is not worth the trouble. The world entire seems to be against Christian's prospects of salvation, but his faith and courage are able to see him through.