What do the letters on the outside of the punnett square stand for

The letters stand for the parents' genotype.  The genotype are the two genes received - one from each parent.
For example, in humans, brown eyes are a dominant trait.  Blue eyes are recessive.  A common way to represent this is with B for brown and b for blue.  (Upper and lower case letters)
A parent may be pure brown  BB - having received two brown genes from each of her parents or bb - having received two blue genes from each of her parents.

A child who is BB will show brown eyes (what they show is call the phenotype)
A child who is bb will show blue eyes
A child who is Bb (get a brown gene from one parent and a blue gene from the other) will be a hybrid but will show brown eyes since brown is dominant over blue.  
If that child who has one of each color (let's say the child is female) becomes an adult and has a child with a male who is also Bb, the chances are one in four that these two people who appear brown eyed can have a blue eyed child.  Punnet square are great for illustrating this.