"Marble Mouth" is a slang term used to signify people who possess a slight speech impediment. It's hard to describe, but it certainly has nothing to do with location or cultural background like one definition ridiculously stated. It's not that they stutter - they don't necessary. But it's obvious that speaking is not their strong suit and they sound as if they have a mouth full of marbles. Marble mouths, more than anything, are highly annoying because you just want them to spit the words out already.
An epic burn. Practice so it will roll right off the tongue and and use when people are drinking so that there will be maximum nasal spewage for effect.
A game in which you each take turns in spitting in each others mouths, as the giver spits into the mouth of the receiver, the receiver has to try to say 'ooky mouth' with a mouthful of the giver's spit.