Old hipster slang
for giving yourself some time to let the alcohol
out of your system; you'd go "on the wagon", either temporarily (if you were a heavy drinker or binge drinker) or one-day-at-a-time permanently ("Hi, my name's Etaoin Shrdlu
, and I'm an alcoholic
It can also be used in reference to any drug, since our options have expanded in the subsequent decades. As has our vocabulary: rehab is a supervised form of drying out, and there's now an industry devoted to that supervision.