Infants take social cues from its parents by taking note of what objects seem important to them. By paying attention to what adults look at, babies begin to learn about language and the emotions of other people. Following another person's gaze is not only a crucial component of human social interactions, but it seems to be uniquely human.
Other animals such as apes might follow each other's gazes, but it appears they're following head movements but not going on to make inferences the way humans do. Around 14 months old, infants begin to notice what other people are looking at.
In fact, in a related study, 14-month old infants not only noticed what adults were looking at, but could distinguish between open eyes and closed, as well eyesight blocked by a cloth. That is, more infants took notice of what the adult was turning toward if that person's eyes were open and uncovered.
"The Eyes Have It: Study Shows Infants More Tuned Into Wider World Than Previously Believed" (Science Daily)