What's past is prologue
. . . Who's the next heir of Naples?
Antonio:The Tempest Act 2, scene 1, 245–254
She that is Queen of Tunis; she that dwells
Ten leagues beyond man's life; she that from Naples
Can have no note, unless the sun were post—
The Man i' th' Moon's too slow—till new-born chins
Be rough and razorable; she that from whom
We all were sea-swallow'd, though some cast again
(And by that destiny) to perform an act
Whereof what's past is prologue; what to come,
In yours and my discharge.
The Tempest is full of theatrical metaphors, such as "what's past is prologue." The metaphor has been forgotten, and the phrase has devolved into distorted forms (like "past and prologue"). When Antonio tells Sebastian that they have the opportunity to "perform an act," he means Act I of their own heroic drama. What's happened so far (that is, "what's past") is the prologue to that play, and the script is henceforth in their hands (in their "discharge").
Prologues were common in Renaissance drama, though Shakespeare himself wrote few of them. The prologue usually set the scene and presented the givens of the play (this is the kind Antonio has in mind). "What's past is prologue," then, translates roughly as "What's already happened merely sets the scene for the really important stuff, which is the stuff our greatness will be made on."
The "act" Antonio proposes is that Sebastian murder his sleeping father, Alonso, King of Naples, and grab the crown. All of them are now "cast" on what they believe is a desert island, so Antonio presumes the crime could easily be covered up. Furthermore, Sebastian's elder sister Claribel is safely out of the way in Tunis; by the time any news of Alonso's death reached her there, newborn boys will have grown thick beards (their chins will be "rough and razorable").