The Great Journey was that undertaken by the first Elves to awaken near the shores of Cuiviénen in Middle-earth. They journeyed then across the great sea and to Aman to live in Valinor.

The Vanyar, the Noldor, and some of the Teleri made the entire journey but some of the Teleri did turn aside and remained in Middle-earth, never seeing the Two Trees of Valinor.
Encyclopedia entry originally written by Nienna-of-the-Valar