This was in the days before electronic calculators, when even mechanical adding machines were expensive and people used tables of logarithms (and trig functions) to calculate. [Think of Manhattan Project days.]

Benford was using a book of such tables (even random numbers came in books, in those days) and noticed that some pages of the book were much more dog-eared than others. That led him to wonder why those particular pages were being used more than others. He discovered that it correlated with the first digit of the numbers. Pages starting numbers with low digits were used more often than pages starting with higher digits.