David Garrick, the writer of this prologue, was one (if not THE) most famous actor and producer of his time. He wrote this prologue as a satire, where the character "Mr. Woodward" would be in mourning, "because comedy is dead", and so they are hoping that Goldsmith's play would make him laugh again. Point in case where he says:
Excuse me, sirs, I pray—I can't yet speak—
I'm crying now—and have been all the week.
"'Tis not alone this mourning suit," good masters:
"I've that within"—for which there are no plasters!
Pray, would you know the reason why I'm crying?
The Comic Muse, long sick, is now a-dying!
Another explanation to the prologue is that, in those days, comedies were not meant to make you laugh, but simply to tell a story with a happy ending. This prologue basically shows that this will be a "first" in theatre, and that times are about to change.
The link provided gives you the prologue in Modern English so you can understand it better.