There's this song by Arctic Monkeys called Crying Lightning when they're singing: "And then offered me your attention in the form of a gobstopper".
... But what does gobstopper mean? I'd been wondering since the day I heard the song :P

Okay - I know that a gobstopper is the candy from the Charlie and the Chocolate Factory book (Willy Wonka and the Chocolate Factory might be the correct title... ), and when Charlie was offered the candy, it was a test. If he took the candy, he lost, if he refused the candy, he won.

So, I just read the lyrics to the song your asking about, and maybe it means like she's offering her attention to the guy, but its like a trick - if he goes for it, he loses, but if he ignores it he wins.

Not quite sure what he would be losing or winning - the girl? Maybe his emotional sanity? (If he ignores her 'gobstopper' he will keep (win) his sanity? If he goes for her 'gobstopper' he will lose, becauses being with her is horrible?? )
(must be honest, never heard of this song before, going out on a limb here... )

Gobstoppers, known as jawbreakers in Canada and the United States, are a type of hard confectionery. They are usually round, usually range from about 1 cm across to 3 cm across (though much bigger gobstoppers can sometimes be found in Canadian/US candy stores, some stores or stands in Europe and many theme parks, up to 8 cm in diameter) and are traditionally very hard.

http://en.wikipedia.org/wiki/Gobstopper