As David discovers from his earliest memories, the gift that he is born with is the ability to telepathically communicate with others of a similar nature, over distance. This is shown at the beginning of the story when David cryptically makes reference to "the others" who he communicates with, one of whom who is his cousin, Rosalind. Note what he says at the beginning of Chapter 6 after David's friend Sophie is captured:
In the evening, when I grew calmer, I found that Rosalind was trying to talk to me. Some of the others were anxiously asking what was the matter, too.
The ability that David has is therefore demonstrated, yet what makes his gift so exceptional is that he is different without bearing any different features or having any noticeable signs of his difference, unlike Sophie. This makes him and the other telepaths special precisely because they cannot be detected by the normal means. This, in a society like Waknuk that is focused so intently on identifying and rooting out any deviations, is a definite advantage as well as a danger.