SOME SAY the custom of bobbing for apples dates all the way back to pre-Christian Ireland and the pagan festival of Samhain, though there's little documentary evidence to support this. Apple bobbing also been popularly associated with Pomona, the ancient Roman goddess of fruits, trees, and gardens in whose honor a festival was supposedly held each year on November first. But that, too, stands on shaky historical ground, apparently, as some question whether such a festival ever actually existed.
We can say with more certainty that the game of apple bobbing goes back at least a few hundred years, that it originated in the British Isles (Ireland and Scotland in particular), and that it originally had something to do with fortune telling. British author W. H. Davenport Adams, who attributed belief in the prognosticative power of apples to "old Celtic fairy lore," described the game as follows in his 1902 book, Curiosities of Superstition:
[The apples] are thrown into a tub of water, and you endeavour to catch one in your mouth as they bob round and round in provoking fashion. When you have caught one, you peel it carefully, and pass the long strip of peel thrice, sunwise, round your head; after which you throw it over your shoulder, and it falls to the ground in the shape of the initial letter of your true love's name.
Other Halloween divination games traditionally played in various parts of Great Britain included "snap apple" similar to bobbing for apples except the fruit is hung from the ceiling on strings and naming nutshells after prospective love interests and placing them near a fire to see which would burn steadily indicating true love and which would crack or pop and fly off the hearth revealing a passing fancy. Accordingly, Halloween used to be known as "Snap-Apple Night" or "Nutcrack Night" in places where these customs were observed.
• Traditional Halloween Divination Games from Ireland - StartPage.ie
• Halloween: An American Holiday, An American History - by Lesley Pratt Bannatyne