By doing these operations repeatedly and in a non-linear manner you end up with a result which can not be used to retrieve the original without the key. Those familiar with chaos theory should see a great deal of similarity to what DES does. By applying relatively simple operations repeatedly a system can achieve a state of near total randomness. DES works on 64 bits of data at a time. For each iteration a 48 bit subset of the 56 bit key is fed into the encryption block represented by the dashed rectangle above.
Decryption is the inverse of the encryption process.
It actually consists of several different transforms and non-linear substitutions. Consult one of the references in the bibliography for details. The limited DES mode available in the freeware version of Enigma modifies the DES standard in two ways. Secondly the data is iterated on only 4 times instead of 16. Nevertheless a naive user would still have to guess on average 2 billion times before the correct key was determined.