Muppet Stayman is simple Puppet stayman but with Opener's 3NT and 3H bids reversed (3NT shows five hearts; 3H denies a 4+ majors). This allows Responder, over 3H, to bid 3S to show 5S/4H, an otherwise unbiddable shape below 3NT when playing Puppet.
So, suppose you have 5S/4H and partner bids 3D. You have both majors, but they are imbalanced. so, bid 3H to show spades. If partner also has spades, he can make sues, which could be nice for slam purposes. If he does not, you can next bid 4H to complete the picture.
Now, suppose that you have 5-5 in the majors. Muppet still works. If partner has a 4-card major, nothing can go wrong. If he has a 5-card major, wow. A lot, you hear 3H. So, bid 3S to show 5S/4H. If Opener declines (3NT), you can bid 4H to complete this picture, as well.