Why was pilgrimages important during middle ages?

Because they were thought to relieve sins if you had been sinful in your life. You see, it's all to do with religion and faith.

The pilgrims would go to a shrine, and pray to God for the dead person. The reason for this is because during that time people could not find any other explanation for things, so they would relate it to magic and God and religion etc. But it would make a lot of sense to a religious person.