'Adam's ale' is a jokey reference to the only drink available to Adam - the first man, in the biblical and Koranic traditions. It alludes to the simplicity and purity of life in the biblical Eden before the fall. This is in contrast to the association of strong drink with evil and the devil. 'The demon drink' was a metaphor frequently used by supporters of the Temperance Movement; a speech made at the Whole World's Temperance Convention, New York, September 1853, included the opinion:
"There is no excuse for the drunkard, and there is much less for the tempter of Drunkenness. He has taken the trade of Satan into his own hands..."
The term 'Adam's ale' is now used less than previously, although it was in common use until the mid to late 20th century. The earliest printed citation is from William Prynne's The soveraigne power of parliaments and kingdomes, 1643:
"They have beene shut up in prisons and dungeons ... allowed onely a poore pittance of Adams Ale, and scarce a penny bread a day to support their lives."
Of course, there has to be a beer with that name. Various ales using the brand name Samuel Adams are brewed by the Boston Beer Company, although to be grammatically correct they are Adams' ales.