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Eljunbyro comes from Old Norse eljun, meaning endurance, and byro, which is generally thought to mean birth. In the series, Eljunbyro is translated as "Endurance's Rebirth", or occasionally "Endurance's Burden".
The symbol representing Eljunbyro consists of a Z with curly ends next to an S-shaped line with three pairs of shorter lines parallell to it, and a parabolic shape opening away from one end of the S with four short lines spreading out of the parabola. The visual symbol itself has not appeared terribly often.
Eljunbyro refers to the role Belle and Pilate play in Rainbow's journey. By recovering her after her "death" in Aridstone, helping her escape the Blue Shelf facility, and (in Belle's case) sharing her memories, the couple gives Rainbow the hope and purpose she needs to continue traveling east. Eljunbyro is also part of Innavedr, the wind that will carry Austraeoh to its goal. Whitemane phrases their role by saying that "...for the pony to head east, endurance must be reborn. Wind is the energy, and the energy will produce a spark, a spark that this world has been waiting for." (Eljunbyro, "Divine Deliverance")
It was first seen while Belle was sequencing with Dash, found in some leaves which fell during the memory of a conversation with Applejack.