The story is a near east creation story. It's intended to explain where we come from, why snakes don't have legs, why human childbirth is so painful, why we know right from wrong. God tells them they will die if they eat the fruit, the serpent says that they won't die, they eat the fruit, they don't die, God finds them and punishes Adam with working the land and eating bread, Woman with painful childbirth and being controlled by men, and the serpent with having no legs, eating dust, and not getting along with people. Then to protect the other magical tree and letting Adam and Eve become fully like the gods (apparently Godhood is simply knowing right from wrong and immortality) he kicks them out and makes a magical fire sword to protect the place.
There's no other theological significance or anything. All the extra eisegesis comes later. The original tale is a creation story in line with Native American stories, "How the Bear Lost its Tail". All cultures have these.
And while it does give rise to the whole fall of man thing, and later the whole Son of God/God sacrifices Himself to Himself to create a loophole in his own system. Because religions keep their baggage. In Genesis being a god is knowing right from wrong and living forever. For fear of them becoming gods they were kicked out etc. Then there's the weird immoral idea that the sins of the father are the sins of the children, hence why Adam and Eve's sin of doing something (which they by definition didn't know was wrong) is passed to all humanity. And because sacrificing animals to forgive sins, what better sacrifice could there be but the sacrifice of a Demigod? Hebrews 9 says almost exactly this. The religion ends up with God sacrificing Himself to Himself (as later Trinitarianism took over and Jesus was said to be one with the father). So each step tends to leave baggage and make it all weirder.
So because of this story with magical trees and talking snakes, mankind is doomed, so to solve this God gives himself a body and kills it. Because only God's own blood had enough magic to allow all-powerful God to create a loophole in his own system. So now, if you accept the story, preferably without questioning it, you can avoid God's first horrible everybody falls short system, and just through God's sacrifice of His blood to Himself, skip that system. So Mahatma Gandhi is burning in hell, because he was Hindu, but Jeffery Dahmer should like his odds because he accepted Jesus and was baptized shortly before his cellmate beat him to death. -- This system is pockmarked with bizarre theological history and crafted towards propagation rather than anything approaching a coherent way of running the universe.