Despite the favorable mixing of blood between elf and human, granting them many advantages and certainly a unique perspective, half-elves are also pitiable in a way. To never truly feel at home, at home, must be indescribable. I suppose this is why so many choose the life of a wanderer. I have been blessed to have many such a companion on the road in my lifetime, and underneath the melancholy is a good heart intertwining the grace of the elves and the ingenuity of humans.
-Excerpt from The Complete Anthropology of Terrania
Half-elves are the offspring of an Elf and a Human, or two humans with some amount of elven ancestry in their lineage. The greater the proximity of the elven ancestor, the greater the likelihood a half-elven child is born, and the more elven their appearance.
Like elves, half-elves require a free elven soul to be born, so humans with distant elven ancestry will much more likely birth a human child, but if an elf soul happens to be free a half-elf child will be born. Even if the chance of a single family conceiving a half-elf is very low, the large number of humans with even a splash of elven ancestry results in a tendency for half-elves to receive these limited elven souls, rather than pure-blooded elves. This causes some tension between half-elves and elves, who believe that the elven soul is wasted upon Zenar (half-elves). Some elves call half-elves Biir, literally translated to "garbage", and a criminal group calling themselves the Children of Corellon hunt down half-elves to capture their souls and transfer them into pure-blooded elf children.
Half-elves born directly of an elf will look perhaps 90% like an elf, the next generation removed perhaps 75%, until the elves are so far back in the lineage as to have been forgotten, whose offspring (if a half-elf is born) will look 50% elf and human.