"Now you're looking for the secret. But you won't find it because of course, you're not really looking. You don't really want to work it out. You want to be fooled."
I feel like this quote really sums up what the movie was about. While some people argue that Angier's final version of The Transported Man was a cop-out, I think they are missing the point of the film. Allow me to take a moment to state that this article will be chalk full of spoilers - so please just watch this great Nolan film if you want some excellent food for thought, and come back to read up on my take afterwards. This is not a movie you want spoiled!
There's no real explanation for how Tesla's machine multiplies Angier - not even a pinning on some as-yet-developed branch of cloning or electrical engineering. Some theories of how teleportation could be possible suggest that it might involve scanning and destroying the original subject, while sending the complete set of DNA to a distant location and creating a complete copy. Alternatively, a copy could be left behind as an undesired side-effect of Tesla's transportation. This is what makes the mechanism so horrifying - Angier doesn't know if he is the original subject being destroyed by drowning in his own trick tank, or if he is the man created in that instant and coming out when it's time for the prestige.
"The secret impresses no one. The trick you use it for is everything."
Beyond being strictly a horrifying concept, Tesla's machine is the only unknown at the end of the film; the only loose end trick that we didn't figure out when we're just dying to know how it's done. But it's like Borden says to Sarah's nephew, "Never show anyone. They'll beg you and they'll flatter you for the secret, but as soon as you give it up... you'll be nothing to them." I think we should be happy - every other trick in the movie has been revealed to be no more than illusion and slight of hand. We should be grateful that there's still a mystery left to be solved at the end of the film. Borden's trick is done with a double, but it's more than that. It's that he and his twin brother share a life so that no one can ever see how he did it. The fake lock on the water tank is revealed to us, we get to see Borden cleaning the remains of the dead bird from its mechanism, and we watch him pull the bullet out of the gun before it's fired. Like Sarah says, "It's really rather obvious once you know how it works". Is that what you expect from Christopher Nolan? For him to propose a really rather obvious explanation instead of leaving you wondering? PAH!
"You never understood, why we did this. The audience knows the truth: the world is simple. It's miserable, solid all the way through. But if you could fool them, even for a second, then you can make them wonder, and then you... then you got to see something really special... you really don't know?... it was... it was the look on their faces..."