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.
If you mosey on over to our "Allusions" list, you'll see that Henry Fielding refers to the ancient Roman poet and critic Horace at least twenty-four times in Tom Jones. That's six more references than he makes to William freakin' Shakespeare, the first runner-up in terms of overall number of citations in this book. So it's not a huge shock to us that Fielding uses a line from Horace as his epigraph to Tom Jones: he clearly loves the guy.
The line Fielding borrows is "Mores hominum multorum vidit," which is Latin for "[he] had sight of the manners [and cities] of many peoples." This phrase comes from Horace's work Ars Poetica, which means The Art of Poetry. It lays out all kinds of do's and don'ts for aspiring poets. Since Tom Jones includes its own series of announcements about what works and what doesn't in writing fiction, again, we aren't too surprised that Fielding borrows a lot of tips and hints from his main man Horace in producing his new guidelines for authors.
As for the meaning of the epigraph, this line is actually Horace's quotation of the great Greek poet, Homer. Horace is complimenting Homer's ability to jump straight into the most important part of his plot lines, without making huge promises that this will be the most exciting story you've ever heard.
Nope, Homer keeps it simple: this will be story of a man who has seen "the manners […] of many peoples." Doesn't this attract your curiosity? Don't you want to know more about these "many peoples" that the hero of Homer's epic poem has seen? And why has he been traveling around so much? By making his poems intriguing and exciting without bragging about it, Homer accomplishes a lot more than lesser poets who keep saying their work is thrilling but who never live up to their hype. Horace admires Homer's straightforwardness, and he wants other poets to imitate it.
Similarly, Tom Jones does not start out with the announcement that this book will tell of the most important events that have ever rocked the kingdom of Britain. The promise of this novel is much lower key: all Fielding swears to us in the first chapter of Book 1 is that he is going to show us the habits of both the lower classes and upper classes. Like Homer's Odysseus, Tom Jones will have observed "the manners" of a broad range of people. But by checking out these varied customs, maybe we will get to something more fundamental, what these "many peoples" share in common: their human natures.