Suppose hackers know all there is to know about Extreme Encryption. Suppose they have the full source code, the executable computer program, and the file that they want to decrypt. Assume everything is on hand except the key that was used to encrypt the file.
Recall that the encrypted file looks like a heap of random bytes, without patterns. The hackers set up many high-power computers to try different possibilities for the first stage of decryption. The problem they run into is that they have no way of recognizing when they did the first stage correctly, should they (contrary to all probabilities) happen to do that first stage correctly. There are no patterns (none, nil, nada patterns!) in the work in process after the first stage.
It's the same after the second stage -- still no patterns. And so on through stages 3, 4, and 5. There are no detectable patterns at the end of the fifth stage. After stage 6, there are very faintly discernible patterns, if the hacker knows what to look for. After stage 7, there is the original text -- provided the right key has been used.
The point: The hacker needs to go through all the stages to check out one key. There is no knowledge along the way of being on the right track. No shortcuts can be detected along the way. It's rather like walking blindfolded. How frustrating for the hacker! How good for our privacy!