A pilgrimage was a journey to a religious location for spiritual significance.
In 2151, Prah Mantoos, a group of his species and a group of Borothan pilgrims ferried by Fraddock made a pilgrimage to the Great Plume of Agosoria and later witnessed the Plume in Enterprise NX-01's mess hall. (ENT: "Cold Front", "Detained")
In 2153, Pri'Nam D'Jamat and his group of Triannon followers took a pilgrimage to the twelfth sphere in the Delphic Expanse, where they encountered Enterprise and eventually took over the vessel. (ENT: "Chosen Realm")
On Terralysium, pilgrimages occured to the White Church shrine in New Eden, although by the mid-23rd century they had dwindled, which was attributed to the battery units powering the building having died. (DIS: "New Eden")