Generally, this song's lyrics seem to point to the state of flux of the U.S during the 60s, as traditional roles of geneder, race, government and religoin were being challenged to their cores.
The song in stanza one asks for all people to "gather round" and "admit" and "accept." These word choices, or diction, are demands to all Americans to come together and see what is actually happening around them and to admit "the waters have grown" or things have changed. The growing waters can also be seen as a reference to a cleansing flood approaching to wash out the old and bring in a new life, so Dylan goes on to warn that you better be ready to swim.
The rest of the lyrics are call outs by Dylan to the old regime in charge who need to recognize and help with a change for the better. He calls out to "writers and critics", "senators, congressmen", and "mothers and fathers" to do what they can to help the youth bring in a bette world or else for this old regime to accept the change and get out of the way.