The Chuckle Bucket is used to describe the area between the base of one's nut sack and their asshole. It is used instead of words like taint or gooch in order to make talking about that areas seem more social acceptable in public.
"Keep talking about my mom like that and I'll kick you in the chuckle bucket."
"Won't be so funny when I ram three fingers through your chuckle bucket."
"THROUGH my chuckle bucket? Ouch."