Answer:
making a pilgrimage
Step-by-step explanation:
Based on the information provided within the question it can be said that the people traveling to the shrines are making a pilgrimage. This term refers to a journey made to a specific (usually spiritual) place, where a person goes to search for meaning in their lives, other's lives, deities, or even a higher good. Which in this case people make the pilgrimage for the healing rituals.