Eye colour is determined by complex genes which determine how much melanin pigment there is in the iris of the eye (see Eye colour facts #1: What causes blue / brown eyes
). Eye colour inheritance is more complicated than when simple charts were used to supposedly predict the eye colour of children based on the eye colour of their parents. Each of our parents gives us one gene forming a pair. No single pair of genes determines eye colour, it is rather a complex interaction of many genes some of which enhance or inhibit the expression of others.
Generally it's likely that two brown-eyed parents will have a brown eyed child and two blue-eyed parents are unlikely to have darker-eyed children. But inheritance is so complex that two blue-eyed parents can have a brown-eyed child and vice versa. And to complicate matters further a baby's blue eyes may turn brown as he / she ages and more melanin is deposited in his / her iris.
Of course there is a spectrum of eye colours from hazel and green through blue to grey ...