Meaning:
Disappear without a trace.

Origin:
Shakespeare came close to this phrase in Othello, 1604:

Clown:

Then put up your pipes in your bag, for I'll away. Go; vanish into air; away!

and in The Tempest, 1610:

Prospero:

These our actors, as I foretold you, were all spirits and are melted into air, into thin air.