Although it's common to see light eyes in animals such as cats, dogs or even parrots, almost all primates have brown or dark eyes (irises). Among primates, which include humans, monkeys, apes and other species there is only one exception to blue eyes, other than humans - black lemurs.
The blue eyes of humans and lemurs is caused by a single nucleotide polymorphism...in simple terms, 'blue' is caused by a single spot in the genes that changed.
The same spot mutated separately in humans and lemurs- this is called convergent evolution. ( mutations can be beautiful!)