BPS Research Digest summarizes recent research on this cute question:
... when the children thought they were invisible by virtue of their eyes being covered, they nonetheless agreed that their head and their body were visible. They seemed to be making a distinction between their "self" that was hidden, and their body, which was still visible. Taken together with the fact that it was the concealment of the eyes that seemed to be the crucial factor for feeling hidden, the researchers wondered if their invisibility beliefs were based around the idea that there must be eye contact between two people - a meeting of gazes - for them to see each other (or at least, to see their "selves").
This idea received support in a further study in which more children were asked if they could be seen if a researcher looked directly at them whilst they (the child) averted their gaze; or, contrarily, if the researcher with gaze averted was visible whilst the child looked directly at him or her. Many of the children felt they were hidden so long as they didn't meet the gaze of the researcher; and they said the researcher was hidden if his or her gaze was averted whilst the child looked on.