Epigraphs are like little appetizers to the great entrée of a story. They illuminate important aspects of the story, and they get us headed in the right direction.
The quality of mercy...
is twice bless'd;
It blesseth him that gives, and him that takes;
'Tis mightiest in the mightiest: it becomes
The thron-ed monarch better than his crown.
This quote from The Merchant of Venice tells us all about the virtues of mercy. It takes place at the climax of the play, where Portia is trying to convince the merchant Shylock to have mercy on the guy who owes him money. Her speech doesn't work there, but it's very appropriate for The Prince and the Pauper.
First of all, we'll translate it for you. According to the quote, mercy blesses twice: first it blesses the person who gives mercy, and then it blesses the person receives mercy. The person most able to be merciful is a person with a lot of power, and it is more important for a ruler to be merciful than to have a lot of money or wear a fancy crown. In other words, it's a good idea to be merciful.
This epigraph speaks almost directly to Prince Edward. The whole point of all the adventures in The Prince and the Pauper is to teach him humility, empathy, and mercy. Edward was willing to kill people without a second thought at the beginning of the novel, but by the end, he's changed so much that he'll be remembered in history for being a merciful and kind ruler.
Since The Prince and the Pauper is a social commentary, this message isn't just for Prince Edward. Mark Twain could mean it to apply to anyone with power and money, at any time, in any country. It also helps us to know that mercy is the most important thing in the whole novel, whatever else might happen along the way to the final page.