I'm sure I'm the only person who doesn't know this, but was there originally only one Daily Double, hence the name?
It was inspired by horse racing where typically there's a pair of races back-to-back where if you can pick both winners you win a larger prize. If it's a long race day (perhaps with ten events) there will be an early and a late double.
Since the game show as we know it existed in three rounds, the Jeopardy round with one double, and Double Jeopardy with two.
(EDIT: You would put down "$2 on the early double, 3 and 7," before the start of the first race of the two. )