what is the most popular time of year for pilgrimages?

I would suppose when the whether was most agreeable. Late spring or summer.

THe narrator describes April rains, the burgeoning flowers and leaves, and the chirping birds. Around this time of year, the narrator says, people begin to feel the desire to go on a pilgrimage. In terms of this pilgrimage Spring/late spring would be the time. Not only is the whether more agreeable there is also a sense of starting over and regeneration in the air.