Question

If both parents have brown eyes, they can either have the genotype BB or Bb. If they both have blue eyes, they must have the genotype bb. If one parent has brown eyes and the other has blue eyes, then one parent must have the genotype Bb, while the other must have the genotype bb.

In summary:
Brown-eyed parents: BB or Bb
Blue-eyed parents: bb
One brown-eyed parent and one blue-eyed parent: Bb and bb, respectively.

Answer 1

The brown version of the eye color gene (B) is dominant over the blue version (b). Dominant means that if either of your genes is the B version, then you will have brown eyes. Genetically speaking, then, people with brown eyes could be either BB or Bb while people with blue eyes could only be bb.