It's a common, longstanding American slang idiom intended to convey that no matter what you've seen, what you are about to see will far top it. It has associations with pop-music and black American culture and expression, but it's a little dated --it has a retro feel to it these days.

Deliberately ungrammatical constructions are often used in pop music and advertising slogans because they are more memorable, convey a sense of "flavor" and seem more fresh and immediate.  In particular, ain't is often used as an intensifier of the negative rather than a reversal of it (double negatives are incorrect in Standard English, but common in black American dialect and many other non-standard English dialects).  You could certainly use the expression casually with a friend, and it can even be used humorously in more formal settings, as in your example.

"You haven't seen anything yet" does have the same superficial meaning, but utterly lacks the attitude of bravado and over-the-top exaggeration.