Famous line from movie Silent Night, Deadly Night 2, in which the maniac killer randomly kills someone while they were taking out the garbage. Look it up on Youtube.
Also, it could be used to describe something that is completely terrible, negative, or unfortunate. Substitute for "Damn that sucks!"
guy 1: "Ah man! Somebody just stole my damn car!"
guy 2: "GARBAGE DAY!"
guy 1: "Man, that girl that I like just had sex with somebody in my bathroom at MY party!"
guy 2: "GARBAGE DAY!!! What a cunt!!!!"