When implementing a payment system, Blockchain.info uses callback URLs with their PHP examples.
I only understand its use of sending the user to a confirmation page after ordering. I have read that it is for added security though too, but I don't see how.
What if I chose not to use it?
If you choose not to, then blockchain.info will not send any message back to your webpage and you may not know when the payment has reached.
If you do not use callbacks, your user would be stuck on the payment confirmation page until someone manually agrees to move him forward.
The added security is that it verifies the payment before sending the customer forward.