Chances are the instant your baby was born, you made eye contact. Eye contact is important in babies because it helps create a bond between the baby and the adult on whom he relies for survival. In fact, scientific evidence indicates eye contact is immensely important in developing the rooting reflex (the reflex that compels baby to search for the mother’s nipple and suckle). 
The average baby starts recognizing people and objects mere moments after they are born, though their eyesight does not develop fully until a few weeks later. However, a baby’s eye development can be positively stimulated by certain patterns, light sources, and colors, which is why many parents hang mobiles above baby’s crib or changing table.
At around six weeks, your baby may make interested eye contact with you and melt your heart.
One of the milestones that a pediatrician looks for when conducting a well-baby checkup at around three months of age is the baby’s ability to follow lights or objects with his eyes. Inability or lack of interest in doing so can indicate a problem with eyesight or a cognitive disorder such as autism. When checking milestones, it is important to remember they are general indicators. Some babies develop certain skills more quickly than others; so, try to be patient if your baby is taking a little longer to hit all those marks.
A rewarding component of eye contact is facial recognition. “The perception of faces, and the understanding that faces can reflect internal states of social partners, are vital skills for the typical development of humans. Of particular importance is processing information about eyes and eye-gaze direction.” 
Babies show fascination with images that resemble faces and will kick and wiggle with excitement. This stimulation indicates a desire to communicate and perhaps anticipation that that face will meet a need for the baby, like retrieve a bottle or change a diaper.
The most important activity taking place in eye contact and facial recognition is the development of a relationship between you and the baby. Not only are you two communicating a contract, wherein baby says I’m going to be the one who needs things and you are the one who will meet those needs, but you are also communicating love and affection, which are equally important needs.
1. Odent, M. The early expression of the rooting reflex. Proceedings of the 5th Int. Congress of Psychosomatic Obstetrics and Gynaecology, Rome, 1977. London: Academic Press: 1117-19.
2. Driver J, Davis G, Ricciardelli P, Kidd P, Maxwell E, Baron-Cohen S. Vis Cogn. 1999;6:509-540.