Most babies are born with blue eyes, the transformation has to do with the protein melanin. Melanin is a brownish pigment that adds colour to hair, eyes, and skin. At the time babies are born, melanin hasn't yet been "deposited" in the eyes' iris. Hence, they appear blue.
After about six months, eyes change colour depending on the amount of melanin. If there is a lot of it, the eyes will turn brown or black. If there is little, they'll stay blue. And if there is no melanin (albinism), then the eyes may appear pink.
Research shows that where one parent has blue eyes and the other has brown eyes, that the child has a 50% chance of having blue and 50% chance of brown. Where the parent with the blue eyes has a lesser blue colour, then the brown will be dominant. For example with brown and blue/green eyed parents, the odds are that the child has 50% probability of brown eyes and 25% probability of green eyes and 25% probability of blue eyes (or 50% blue/green). About half of the children with brown eyes will carry the Green allele for the gey gene (common gene for eye colour ), and the other half will carry the blue allele, so their children may have blue, green or brown eyes.