Why do people look in the face or eyes while communicating?
Eye contact is one of the principal cues humans use to evaluate where other people direct their attention. A special issue on the use of eye tracking in the Infancy journal and other studies reported that infants' eyes are useful measures of attention over a range of task domains including object perception (Johnson, Slemmer, &amp; Amso, 2004), faces (Hunnis &amp; Geuze, 2004), and categorization (McMurray &amp; Aslin, 2004). 

This relationship between eyes and attention begins developing as early as within the first couple of neonatal weeks (Lohaus, Keller and Voelker, 2001). For the same reason, eye- and gaze tracking are central measures in many areas of the cognitive sciences, including developmental (neuro)psychology, perception and working memory. 

Because gaze is such a good general indicator of attention, mutual eye contact between myself and someone indicates that we are both attending to one another, if not always, then at least often enough to depend on.

References


Lohaus, A., Keller, H., &amp; Voelker, S. (2001). Relationships between eye contact, maternal sensitivity, and infant crying. International Journal of Behavioral Development, 25(6), 542-548.
Hunnis , S. and Geuze , R. H. 2004. Developmental changes in visual scanning of dynamic faces and abstract stimuli in infants: A longitudinal study. Infancy, 6(2): 231–255. 
Johnson, S. P., Slemmer, J. A., &amp; Amso, D. (2004). Where Infants Look Determines How They See: Eye Movements and Object Perception Performance in 3‐Month‐Olds. Infancy, 6(2), 185-201.
McMurray , B. and Aslin , R. N. 2004. Anticipatory eye movements reveal infants' auditory and visual categories. Infancy, 6(2): 203–229.