adfgvx, was a creation of Col. Fritz Nebel and introduced in June 1918 was the successor to adfgx which was introduced in March of that year.
It was a pencil and paper system, which was used as a 'field cipher', i.e. by people at the front.
The earlier adfgx could be used to encode a 25 letter alphabet, like playfair this meant that for a 26 letter alphabet, some two letters would be encoded the same way.
On the other hand, adfgvx could encode a 36 letter alphabet - enough for 26 letters plus 10 digits!
Both adfgx and adfgvx was used by the Germans in World War I, and was a highly successful field cipher. A general way to analyse it was not found until long after the war ended, though ways were found to break it based on known plaintexts, i.e. standardised parts of the underlying message. The French officer, Lt. Georges Painvin worked out methods to break the cipher during the war.
adfgvx was a two stage cipher. The first stage used a grid which converted each letter of plaintext into a pair of letters, which came from the set adfgvx
The arrangement of letters in this grid formed part of the key and would be kept secret. One might have a set of rules for filling out the grid based upon some keyword if the key needed to be memorised. The key for the gris is called the 'fractionating key'.
Thus, each letter of the message would be encoded by a digraph, a pair of letters.
Using this grid, the word 'attack' would become dd va va dd ga ag
So far this is simply a monoalphabetic cipher, and easily crackable given enough text. However, this stage would be followed by a columnar transposition stage, where the letters would be scrambled.
Thus, using the keyword, 'code' as a 'transposition key' we get:
Thus the final message for our table and keyword becomes adgd aavd agvg
This is hard to analyse due to the fact that there is little redundancy in the symbols used, and even when one realises that it's based upon blocks of two letters there is the issue of working out which two letters are to be taken as one 'block'
Of course, the length of the keyword for the transposition stage might be anything (limited by manageability)!
The transposition key and fractionating key were changed each day according to a pre agreed schedule.
One question remains, and that is 'Why the Letters a, d, f, g, v and x?
This is simply as when transmitted by morse, these sound quite distinct to the trained ear, and so the chances of transmission errors are reduced.
A .- D -.. F ..-. G --. V ...- X -..-