A punnet square is a diagram which helps to predict the offspring of two individuals (human or animal). This is based upon dominant and recessive genes.
In example one, a mother has brown eyes (represented by Bb). The "B" represents the dominant gene of brown eyes, and the "b" represents a recessive green-eyed gene. For ease, the father possesses the same. A punnet square which illustrates the eye color of their offspring will look like this (the single letters across the top represent the mother and the single letters down the left side represent the father):
B BB Bb
b Bb bb
In the above case, the child has a 75% chance of inheriting brown eyes (BB, Bb, and Bb) and a 25% chance of inheriting green eyes (bb).
To provide another example, let us change both the mother's and father's genes regarding eye color. Here, the mother will have BB (both dominant brown genes) and the father will be green-eyed, represented by bb. The punnet square for this will look like this (same setup as before-mother across the top; father down the left side):
b Bb Bb
b Bb Bb
In this case, the child of the couple has a 100% chance of inheriting brown eyes (since each "square" contains a dominant and recessive gene). The is no chance the child will have green eyes (no double recessive pairing exists in this square).