pilgrim (noun) – someone who travels around or a traveller to a holy place
pilgrimage (noun) – a trip to a holy place
Here are some examples of how you can use it:
Visiting this unknown region in my country I felt like a pilgrim travelling in foreign lands.
Many pilgrims come to Jerusalem to visit the purported (= assumed) place of Jesus Christ’s grave.
My neighbour put “Haj” in front of his name after he made a pilgrimage to Mecca.