Dapper's the very first chump we meet in this play. He's a young, snazzy dressing (dare we say dapper) law clerk who loves to gamble. Face meets him at a tavern and tricks him into believing that Subtle is a doctor who can use magic to help him up his gambling game.
Dapper's willing to pay Subtle to conjure up a "familiar" (a spirit that helps people practice magic—think witches' black cats) to help him win a bunch of money (1.1.190-193).
This is a pretty mind-boggling lack of imagination, in our humble opinions. If you think you're getting a familiar, wouldn't you use it to do things other that win big at the high stakes table? But imagination—or intelligence—isn't Dapper's strong suit.
He usually only speaks in very short lines, and when he does speak he's often saying something like this:
"By Jove, sir,
I'll win ten thousand pound, and send you half.
I' fac's no oath." (1.2.201-203)
Oh, Dapper. You're such a dolt.
Dapper's a stereotype: the unimaginative, clueless cheeseball. His modern day descendants include Vince Vaughn's character from Swingers and any guy who wears a fedora outside of a costume party.
But Dapper's delusional enough to believe that his modern-day descendants would include all eleven, twelve, or thirteen of Danny Ocean's gang, Humphrey Bogart in anything, or the Wolf of Wall Street himself.
In other words, he's totally bored with his professional career and wants some excitement in his life. Being a law clerk is a total snooze for Dapper, which is why he spends all his spare time gaming at the local hangouts.
And that's why it's so easy for Subtle and company to "gull" Dapper out of a bunch of money. They play on his fantasies and desires to live a large, exciting life and wind up tricking him into believing that he's so special that the Queen of Fairies wants to help him become the richest dude in London...for a small fee, that is.
By the way, in English folklore, the Fairy Queen rules over all the other fairies‚ after all, she's the dang queen. According to historian Keith Thomas, an absolute ton of English folks got duped out of money in the late 16th and early 17th Centuries because they believed that fairies could help them get rich. (Source: Religion and the Decline of Magic: Studies in Popular Beliefs in Sixteenth and Seventeenth-Century England, 1991)
Of course, the Fairy Queen doesn't really exist (sorry to break it to you) but Dapper really, really, really wants to believe that she does. When Doll Common dresses up and plays the role of the Fairy Queen, Dapper's totally convinced that he's hit the jackpot.
Unfortunately, this dude ends up being put through a bunch of humiliating rituals while the conmen pick his pockets before gagging his mouth and stashing him in a privy (or outhouse—eew) while they sucker some other chumps out of money.