Elder Days was a term that, during the Second and Third Age, referred to the First Age and before. However, 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.
Tolkien notes that the word "Elder" has deliberately an archaic flavour, since it is now only applied to persons (Elders = seniors). He also pointed to an association with the poetic word eld 'old age, antiquity'.
Early English had the expression Þe eldern dawes 'in the days of our forefathers, long ago, Days of the Seniors'.