Ask most people what they notice first, and it's usually the eyes. It's not just some weird thing, though it is uniquely human -
perhaps thanks to evolution:
Humans are also the only primates for whom the outline of the eye and the position of the iris are clearly visible. In addition, our eyes are more horizontally elongated and disproportionately large for our body size compared to most apes. Gorillas, for example, have massive bodies but relatively small eyes.
The cooperative eye hypothesis explains these differences as traits that evolved to help facilitate communication and cooperation between members of a social group. As one important example, human mothers and infants are heavily reliant on eye contact during their interactions. One study found that human infants look at the face and eyes of their caregiver twice as long on average compared with other apes.
So eye contact isn't only a cliche - we're made for it!