What is the story behind the phrase "close but no cigar" ?

Cigars were a common prize at fairs and carnivals.

I heard it comes from that old state fair game where you whack a seesaw with a hammer and send a disk flying at the bell. Apparently the prize for that game always used to be a cigar. Hence if you got the disk almost all the way there you were close, but you didn't get a cigar. And from this comes "close, but no cigar."

A number of online sources are pointing to its most likely origin as being early and mid-twentieth century carnivals, when cigars would be given out as prizes.

Close but no cigar

Meaning: Nearly achieving success, but not quite.
Example: That free throw was close but no cigar.
Origin: Carnival games of skill, particularly shooting games, once gave out cigars as a prize. A contestant that did not quite hit the target was close, but did not get a cigar. :)las08

The phrase, and its variant 'nice try, but no cigar', are of US origin and date from the mid-20th century.
Fairground stalls gave out cigars as prizes, and this is the most likely source, although there's no definitive evidence to prove that.