Symbolism, Imagery, Allegory
Okay, yeah, Socrates is a character—and a character based on a real person, at that. So, how could he possibly be a symbol, too? Can one man be so many things? Answer: absolutely. Yes, he has significance in history and character-wise, but in this play, he and his "school" also symbolize certain practices in education and rhetoric that Aristophanes is trying to critique.
Strepsiades's first description of the Thinkery and its mission give us a decent sense of what Aristophanes's objections to this school of thought might be:
"That house is a Thinkery for clever souls. / Some gentlemen live there who argue that the sky / is a casserole-cover—and make us all believe it— / and that it covers us all, and we're charcoal briquets. / These people train you, if you pay them money, to win any argument, whether it's right or wrong." (94-98)
It sounds pretty funny, but it's also biting—imaging having your lessons and high-level thought compared to basically hypnotizing someone and telling them to cluck like a chicken. That's a party trick that serves no purpose, and so (in Aristophanes's view) is the kind of education that Socrates offers—and of which this entire play is a send up.