In the fiction of J. R. R. Tolkien, the Elder Days are the first Ages of Middle-earth.
During the Second and Third Age, the term referred to the First Age and before, but in the Fourth Age the term began to be applied to all three ages which came before: a time before the dominance of Men and the dwindling of the Elves and other races.
Computer users' slang
In some computer users' slang "the Elder Days" means the period before about 1980, before many modern computer developments started. This usage started among computer programmers who were familiar with Tolkien's writings.
References
Elder Days Wikipedia(Text) CC BY-SA