What does "青年文明号" mean?
号 is a common designation word for naming man-made vehicles like  ships, planes and trains. 

For example:

Ronald Reagan = 罗纳德·里根

USS Ronald Reagan = 罗纳德·里根号 (super-carrier named after Ronald Reagan)

“青年文明号" is a youth organization that emphasize on "Youth movement " And the word 号 in the organization's name signified this fact. 

It is in fact, comparing itself to a ship or train (Something that move purposefully ; a vehicle for advancing development )