This expression is more usually spoken as ‘the stuff of dreams’.
In the magician Prospero’s speech in The Tempest he alludes to the gods and spirits in the play, which are imagined and apt to blow away in a puff of smoke. Shakespeare is also playing with the idea that the play itself evokes and requires a suspension of disbelief on the part of the audience, which also soon melts away when the play is ended and the characters return to being real life actors..