Symbolism, Imagery, Allegory
They're in the title, they're central to the action in the play, and they're definitely not just one of those white fluffy things that sometimes looks like a walrus.
Rather, they're legit characters that play an active role in the whole drama of Strepsiades going to Socrates and trying to learn the art of rhetoric. They also function as the chorus, commenting on what goes down and suggesting what the characters could or should be doing.
Beyond that, though, they are also quite literally part of the up-in-the-air theories that Socrates is mingling with when Strepsiades finds him suspended in he air, engaged in reflection. When Socrates is up there in the clouds and ether, that really means he's immersed in his own thoughts and philosophizing.
He draws a connection between air and moisture and his "deep thoughts" when he explains to Strepsiades why he's so high up:
"Never / could I make correct celestial discoveries / except by thus suspending my mind, and mixing / my subtle head with the air it's kindred with. / If down below I contemplate what's up, / I'd never find aught; for the earth by natural force/draws unto itself the quickening moisture of thought. / The very same process is observable in lettuce." (228-234)
There's an analogy between the clouds and Socrates's thoughts here; just as the clouds are slippery, insubstantial, and hard to get a grasp on, so Socrates's teachings are portrayed as, er, less than weighty (and certainly slick). So there you have it—totally separate from their role as the Chorus in playing around with Strepsiades's life, they actually represent the superficiality of Socrates's thoughts