The idea is to be either the 10 billionth app downloader, or the first person to submit a non-purchase entry form (available here) immediately after the 9.999,999,999th download.
It's not the first time Apple has run such a contest. In fact, most of their milestones like this usually have some sort of promotion attached.
You need to be over 13 years of age (or obtain a parent’s or legal guardian’s consent before participating) and you need to be a “legal resident of a participating App Store country” in order to qualify.
