Consider the opening details about the season. Why would spring make people "long to go on pilgrimages"?
The evocation of Spring at the beginning of The Canterbury Tales places Spring and the seasons in a cyclical time frame. The lyricism with which the narrator evokes the sights and smells of Spring are really stunning, which is why we might be slightly surprised when the narrator breaks out of this mode to talk about pilgrimages - a love story might have been a more fitting evolution for this tale! However, a link is made between nature which follows a set cyclical route and humans, who want to experience freedom after the confinement imposed upon them by the harshness of winter and so therefore go on pilgrimages in Spring to enjoy the weather. Of course, going on pilgrimages was also a holiday, not just about penance, so there is also a vivid, lively, profoundly social side to the decision to go on a pilgrimage.