The Avari are Those who Refused the Summoning of Oromë, or simply The Unwilling. Half of the Avari came from the largest tribe, the Nelyar, but most of the Nelyar went on the journey. Half of the Tatyar remained as well.
After the Separation the Avari became divided even more than the Eldar, though little of their history became known to the Elves and Men of the West of Middle-earth. At least six kindreds existed, and they continued to call themselves 'Quendi', considering those who went away as deserters. Some of these tribes later also journeyed westward, intermingling with the Nandor, and a few even reached Beleriand, though usually remaining in unfriendly relationship with the Sindar.
Read more about this topic: Sundering Of The Elves