I'll give you a basic idea so you have something to work from.
Plato's allegory of the cave is that human beings are unable to grasp the true realities of the world. They see only the shadows of the world. The true world is a perfect one, and all the knowledge in this world is hidden from view for the human beings who live in the cave. They can only catch glimpses of it and make up theories about what they see.
http://www.ship.edu/~cgboeree/platoscave.html
Creationists argue that the world was created by God. Man was created in his image. We can never understand God's purpose for doing this, nor can we fathom the powers he has that enables him to do this. We can make up theories and ideas about God, but we cannot ever fully understand him.
The real analogy, as I see it (personal opinion), is that both stories require a leap of faith and a struggle for forbidden knowledge. The humans in the cave assume that there is a better world out there, but they cannot be sure. They can only believe so. They dare not venture into it because they fear they will be burnt by the flames covering the exit (fear of gaining knowledge). The same goes for God - as human beings we cannot understand him. We must not try to learn too much about God. Knowledge is not good for us - in fact, God thinks knowledge is something that makes human beings sinners, because it makes us be like him (as is evidenced by the eviction from Heaven after the snake tempts Eve into eating an apple from the tree of knowledge).
So both stories show that the search for truth is dangerous and requires that human beings break the shackles they are bound by - in Plato's cave these are real chains, in creationism these are the knowledge God hides from us, and the fear of God's wrath if we do something wrong. And in both stories those shackles are not broken, so the truth is not revealed.